Since the question asks what "must be true," the correct answer is something that will ALWAYS happen.

From the question stem, we know Sandra and Wallace must write on this news item. The contrapositive of the fourth global rule tells you that when Sandra (or Phillip) writes on a news item, Roger does not write on the news item. So we know Roger will never write on this news item.

The contrapositive of the first global rule tells you that since Roger does not write on this news item, Marco also does not write on this news item.

The contrapositive of the second global rule tells you that since Marco does not write on this news item, Vicki also does not write on this news item.

So far you know that Sandra and Wallace must write on this news item. You also know that Roger, Marco, and Vickie must not write on this news item. This allows you to eliminate the choices that say Marco and Roger also write on the news item, since we just proved they can never do so.

Nora and Phillip are still undetermined. You know, based off the third global rule, that at least one of them (either one) must write on the news item, but it's also possible that both of them write on the news item. This means you can eliminate the choice that says Nora does write on the news item and the choice that says Phillip does not write on the news item, since each of these could be true, but are not always true.

This leaves you with the correct answer, which we have shown is always true: Vicki does not write on the news item.

Based on the first global rule, you know that a valid outcome must include either orange or white. It can never include both. Therefore, you can eliminate "blue, green, orange, white" because it includes both orange and white.

Based on the second global rule, you know that a valid outcome must include either red or yellow. It can never include both. Therefore, you can eliminate "green, orange, red, yellow" because it includes both red and yellow.

Based on the third global rule, you know that if white is used, blue must also be used. Therefore, you can eliminate "green, red, violet, white" because white is used, but blue is not included.

Based on the fourth global rule, you know that if violet is used, yellow must also be used. Therefore, you can eliminate "blue, red, violet, white" because violet is used, but yellow is not.

The correct answer is green, orange, violet, yellow. It meets every one of the global rules.

The restriction of green not being used actually gives you a lot of information. You know that one color must be orange or white, and that a second color must be red or yellow. This means the remaining two colors must be chosen from the three colors of blue, green, and violet.

Since you know that green is not being used for this problem, that means blue and violet must both be used:

___, ___, blue, violet

The fourth global rule also tells you that since violet is used, yellow must also be used:

___, yellow, blue, violet

The fourth color can be either orange or white:

orange/white, yellow, blue, violet

Now you are looking for an answer choice that has two colors that must be used in this set-up (you have three that must be used: yellow, blue, violet). The correct answer is blue and yellow, since they both must be used.

Since orange is not used, you know from the first global rule that white must be used. Furthermore, since white is used, you know from the third global rule that blue must also be used:

white, blue, ___, ___

For the third color used, it could be either red or yellow, based on the second global rule.

If it is red, the fourth color must be green. Violet is the only other possible color that could be the fourth color, but it cannot be used in this case, because if violet is used, so must yellow, based on the fourth global rule. This gives you one possible selection:

white, blue, red, green

If yellow is used instead of red, this gives you two more possible selections. Either green or violet can be the fourth color used:

white, blue, yellow, green

white, blue, yellow, violet

So, in total, there are three possible different groups of four colors.

For this problem, you are looking for a pair of colors that can never be used together. If you can show that a pair of colors can be used together to result in a valid outcome, you can eliminate that as a possible answer.

You can eliminate blue and yellow because the following selection is possible and valid: white, yellow, blue, green.

You can eliminate red and white because the following selection is possible and valid: white, red, yellow, blue.

You can eliminate violet and white because the following selection is possible and valid: white, yellow, violet, blue.

You can eliminate white and yellow because the following selection is possible and valid: white, yellow, violet, blue.

The correct answer is red and violet. If red is used, yellow cannot be used, based on the second global rule. But if violet is used, yellow must be used, based on the fourth global rule. This conflict tells you a valid selection cannot be created by using both red and violet.

You are looking for a pair of colors from which at least one of the two colors must always be used. You can eliminate wrong answers by showing that neither of the colors in a pair has to be used, by giving one possible selection that includes neither.

Violet and yellow can be eliminated because you could have the selection of orange, red, green, blue.

Green and white can be eliminated because you could have the selection of orange, yellow, blue, violet. 

Violet and white can be eliminated because you could have the selection of orange, red, green, blue.

Orange and violet can be eliminated because you could have the selection of white, red, blue, green.

The correct answer is blue and green. At least one of these two colors must always be used (it's worth noting that it's possible both are used). If neither blue or green are used, there is no way to use four total colors. You would have:

1) orange or white
2) red or yellow
3) violet

But by not using blue or green, there is no possible fourth color - resulting in an invalid set-up.

For this problem, you are looking for the pair of colors that, if used, will allow only one possible combination of four colors to be used.

Blue and red can be eliminated. If these two are used, you still can use either white or orange, so there is more than one possible selection.

Blue and violet can be eliminated. If these two are used, you can still use either white or orange, so there is more than one possible selection.

Blue and white can be eliminated. If these two are used, you can still use either red or yellow, so there is more than one possible selection.

Green and yellow can be eliminated. If these two are used, you can still use either white or orange, so there is more than one possible selection.

The correct answer is green and violet. If violet is used, then based on the fourth global rule, yellow must also be used. This leaves the choice between either white or orange for the fourth color. Since blue is not being used, based on the third global rule, white cannot be used - so orange must be used:

orange--yellow--green--violet

For this problem, you are looking for an outcome that can be false. Another way of looking at this is something that can be untrue or something that could possibly not happen. If the outcome must be true then it is not the correct answer here.

"Nancy must learn violin if Pete learns violin" is always true, so this is not the correct answer. If Pete learns to play violin, the fourth global rule tells you that Max must also learn to play violin. Then, the first global rule tells you that Nancy must also learn to play violin. So this outcome cannot be false.

This also leads you to your correct answer: Raina must learn cello if Pete learns violin. You just showed that if Pete learns violin, Max and Nancy must also learn to play violin. This means that Raina and Trig must learn the same instrument, to keep with the fifth global rule.

Since the third global rule tells you that Trig can learn either cello or flute, the two of them could learn either instrument. Since they can learn to play flute, this makes the statement that "Raina must learn cello if Pete learns violin" a can-be-false outcome.

For this problem, you can eliminate each of the four wrong answers by going through the global rules given at the beginning of the problem.

The first global rule tells you that Max and Nancy must learn to play the same instrument. Based on this, you can eliminate the answer choice that has Max learning flute and Nancy learning violin.

The second global rule tells you that Pete and Raina do not learn to play the same instrument. Based on this, you can eliminate the answer choice that has both Pete and Raina learning cello.

The fourth global rule tells you that if Pete learns to play violin, Max must also learn to play violin. Based on this, you can eliminate the answer choice that has Pete learning violin and Max learning cello.

The fifth global rule tells you that no one learns to play an instrument alone. It's also important to note that this does not necessarily mean every instrument must be learned to be played - merely that no one learns alone. Based on this, you can eliminate the answer choice that has Raina learning violin alone.

The correct answer is: Max, Nancy, and Pete learn flute, and Raina and Trig learn cello. This arrangement follows all global rules.

For this problem, you are looking for the situation that must always be true. If you can show that the situation does not necessarily have to happen, you can eliminate it as an answer choice.

You can eliminate wrong answers by setting up hypothetical outcomes. If you have Max and Nancy learn cello (the first global rule tells you they must learn together) as well as Pete learn cello, then Trig and Raina learn flute, you can eliminate a few wrong answers.

Cello: Max, Nancy, Pete
Flute: Trig, Raina
Violin: None

You can eliminate "If any of the students learn cello, exactly two of the students do" because you just proved three students can potentially learn cello.

You can eliminate "If any of the students learn cello, Trig learns cello" because you just proved if some students learn cello, Trig can learn flute. 

You can eliminate "If any of the students learn flute, exactly three of the students do" because you just proved two students can potentially learn flute.

The other two possible answers have to do with learning violin. You can prove that Pete does not necessarily have to learn violin if some students learn violin, so that you can eliminate that answer. If Max, Nancy, and Raina learn violin, that can leave Trig and Pete to learn Flute.

Cello: None
Flute: Trig, Pete
Violin: Max, Nancy, Raina

This leaves you with the correct answer, something that must always be true to reach a valid outcome: If any of the students learn violin, exactly three of the students do.