All GRE Subject Test: Math Resources
Example Questions
Example Question #21 : Real Analysis
Evaluate
A complement symbol means you want to only include the numbers in the universal set that do not appear in the set being complemented.
However, all the numbers in the universal set appear in itself. This means the complement of ANY universal set is the empty set.
Example Question #141 : Other Topics
Evaluate
Always work in parentheses first. First, you need to solve the union of sets A and B. Union means to include everything in both sets without repeating any duplicates.
Now take the complement of this by including the numbers in the universal set that do not appear in A union B. This leaves
Example Question #2 : Complements
If angle , find angle if angles and are complementary.
Step 1: Recall the definition of Complementary angles.
Two angles are complementary if the sum of the two angles is ALWAYS .
Step 2: If the sum of the angles is , then we can subtract the other one to find the missing angle...
So,
Example Question #141 : Other Topics
Using DeMorgan's law, which of the following is equivalent to the statement
The easiest way to remember DeMorgan's law is that you flip the symbol upside down (which changes union to intersection and vice versa), complement both sets (remembering that the complement of a complement is just that set), and either remove parentheses or add parentheses and place the complement symbol outside of it
Flip the intersection symbol to a union, complement both sets, and add parentheses with the complement symbol outside of it.
Example Question #142 : Other Topics
Use DeMorgan's law to write a statement that is equivalent to the following statement
The easiest way to remember DeMorgan's law is that you flip the symbol upside down (which changes union to intersection and vice versa), complement both sets (remembering that the complement of a complement is just that set), and either remove parentheses or add parentheses and place the complement symbol outside of it.
Flip the symbol from an intersection to a union, complement both sets, and remove the parentheses.
is equivalent to the original statement
Example Question #143 : Other Topics
Using DeMorgan's law, is the statement equivalent to ? If not, choose the correct statement that is equivalent.
No, the equivalent statement is
No, the equivalent statement is
Yes, the statements are equivalent.
No, the equivalent statement is
No, the equivalent statement is
Yes, the statements are equivalent.
The easiest way to remember DeMorgan's law is that you flip the symbol upside down (which changes union to intersection and vice versa), complement both sets (remembering that the complement of a complement is just that set), and either remove parentheses or add parentheses and place the complement symbol outside of it.
Flip the union symbol to an intersection, complement both sets, add parentheses and a complement symbol outside the parentheses.
Example Question #144 : Other Topics
Using DeMorgan's law, is the statement equivalent to ? If not, choose the correct statement that is equivalent.
No, the equivalent statement is
Yes, the statements are equivalent.
No, the equivalent statement is
No, the equivalent statement is
No, the equivalent statement is
No, the equivalent statement is
The easiest way to remember DeMorgan's law is that you flip the symbol upside down (which changes union to intersection and vice versa), complement both sets (remembering that the complement of a complement is just that set), and either remove parentheses or add parentheses and place the complement symbol outside of it.
Flip the union symbol to an intersection symbol, complement both sets, and remove the parentheses
Example Question #145 : Other Topics
Using DeMorgan's law, which of the following is equivalent to the statement
The first step is to realize that the C and intersection symbol in the original question are distractions and have nothing to do with applying DeMorgan's Law.
In the parentheses, flip the symbol from an intersection to a union and complement both sets.
Normally, with only two sets, you should eliminate the parentheses that was there to show that the complement symbol applied to the entire parentheses. However, with three sets you still need to know the order in which to work out the problem so you should keep the parentheses around B and A.
Example Question #146 : Other Topics
Using DeMorgan's law, is the statement equivalent to ? If not, choose the correct statement that is equivalent.
No, the equivalent statement is
No, the equivalent statement is
Yes, the statements are equivalent
No, the equivalent statement is
No, the equivalent statement is
No, the equivalent statement is
The easiest way to remember DeMorgan's law is that you flip the symbol upside down (which changes union to intersection and vice versa), complement both sets (remembering that the complement of a complement is just that set), and either remove parentheses or add parentheses and place the complement symbol outside of it.
Flip the union symbol to an intersection symbol, complement both sets, and remove the parentheses.
Example Question #1 : Logical Equivalence
Suppose A, B, and C are statements such that C is false if exactly one of A or B is true. If C is true, which of the following is also true?
Both A and B are True
A is false, B is true
A is true, B is false
Both A and B are both False
Both A and B are both False
Step 1: Let's break down the logic problem...
C is false if A or B is True.
Example: C-False, A-True, B-False.
Step 2: Try to find what happens if C is true
If C is true, "or" changes to "and", and True becomes false..
So: C-True, A-False, B-False..
A and B must both be false for C to be true..
Answer: Both A and B are False.