GRE Quantitative Flashcards: Sets Venn Diagrams

What this deck covers

This deck focuses on Sets Venn Diagrams, giving you a quick way to review the definitions, rules, and examples that matter most for GRE Quantitative.

How to use these flashcards

Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

Flashcard 1: What is the relationship between $A\setminus B$ and $A\cap B^c$?

Answer: $A\setminus B=A\cap B^c$. Expresses set difference as the intersection of A with the complement of B.

Flashcard 2: What is the definition of the symmetric difference $A\triangle B$?

Answer: $A\triangle B=(A\setminus B)\cup(B\setminus A)$. Defines the symmetric difference as the union of elements in A but not B and elements in B but not A.

Flashcard 3: Find $|A\cup B|$ if $|U|=50$ and $|(A\cup B)^c|=12$.

Answer: $38$. Determines union size by subtracting the complement from the universal set: $50 - 12 = 38$.

Flashcard 4: State the formula for the size of a union: $|A\cup B|$ in terms of $|A|,|B|,|A\cap B|$.

Answer: $|A\cup B|=|A|+|B|-|A\cap B|$. Applies the inclusion-exclusion principle to count elements in the union without double-counting the intersection.

Flashcard 5: Find $|A\triangle B|$ if $|A|=14$, $|B|=11$, and $|A\cap B|=5$.

Answer: $15$. Computes symmetric difference as sum of exclusive parts: $(14-5) + (11-5) = 15$.

Flashcard 6: Find $|B\setminus A|$ if $|B|=19$ and $|A\cap B|=6$.

Answer: $13$. Computes set difference as elements only in B: $19 - 6 = 13$.

Flashcard 7: Find $|A^c|$ if $|U|=60$ and $|A|=22$.

Answer: $38$. Calculates the complement as elements not in A: $60 - 22 = 38$.

Flashcard 8: What is the definition of the intersection $A \cap B$ in set notation?

Answer: $A \cap B=\{x: x\in A\text{ and }x\in B\}$. Defines the set containing all elements that belong to both A and B.

Flashcard 9: Find $|A\cap B\cap C|$ if $|A\cap B|=9$, $|A\cap B\setminus C|=6$.

Answer: $3$. Determines the triple intersection by subtracting the part excluding C: $9-6=3$.

Flashcard 10: What does it mean to say $A\subseteq B$?

Answer: Every element of $A$ is in $B$. Indicates that A is a subset of B, meaning all elements of A are also elements of B.

Flashcard 11: Find $|A\cap B|$ if $|A|=20$, $|B|=17$, and $|A\cup B|=30$.

Answer: $7$. Solves for intersection using inclusion-exclusion rearranged: $20 + 17 - 30 = 7$.

Flashcard 12: Find $|A\setminus B|$ if $|A|=25$ and $|A\cap B|=9$.

Answer: $16$. Computes set difference as elements only in A: $25 - 9 = 16$.

Flashcard 13: Find $|U\setminus(A\cup B)|$ if $|U|=80$, $|A|=35$, $|B|=30$, and $|A\cap B|=10$.

Answer: $25$. Calculates elements outside the union: $80 - (35+30-10)=25$.

Flashcard 14: Find $|A\cup B|$ if $|A|=18$, $|B|=15$, and $|A\cap B|=7$.

Answer: $26$. Calculates the union size using inclusion-exclusion: $18 + 15 - 7 = 26$.

Flashcard 15: What is the definition of the complement $A^c$ relative to universal set $U$?

Answer: $A^c=U\setminus A=\{x\in U: x\notin A\}$. Defines the set of elements in the universal set U that are not in A.

Flashcard 16: What is the definition of the set difference $A\setminus B$?

Answer: $A\setminus B=\{x: x\in A\text{ and }x\notin B\}$. Defines the set of elements in A but not in B.

Flashcard 17: What is the definition of the union $A \cup B$ in set notation?

Answer: $A \cup B=\{x: x\in A\text{ or }x\in B\}$. Defines the set containing all elements that belong to A or B or both.

Flashcard 18: State De Morgan's law for the complement of an intersection: $(A\cap B)^c$.

Answer: $(A\cap B)^c=A^c\cup B^c$. States De Morgan's law, equating the complement of an intersection to the union of complements.

Flashcard 19: What does it mean to say two sets $A$ and $B$ are disjoint?

Answer: $A\cap B=\varnothing$. Indicates that A and B have no elements in common, so their intersection is the empty set.

Flashcard 20: State the 3-set inclusion–exclusion formula for $|A\cup B\cup C|$.

Answer: $|A\cup B\cup C|=|A|+|B|+|C|-|A\cap B|-|A\cap C|-|B\cap C|+|A\cap B\cap C|$. Applies the inclusion-exclusion principle for three sets to count the total unique elements in the union.

Flashcard 21: State De Morgan's law for the complement of a union: $(A\cup B)^c$.

Answer: $(A\cup B)^c=A^c\cap B^c$. States De Morgan's law, equating the complement of a union to the intersection of complements.

Flashcard 22: Identify the set represented by "in exactly one of $A$ or $B$" using set notation.

Answer: $(A\setminus B)\cup(B\setminus A)$. Represents elements that are in exactly one of the sets A or B, forming the symmetric difference.

Flashcard 23: Find $|A\cap B^c|$ if $|A|=16$ and $|A\cap B|=9$.

Answer: $7$. Calculates elements in A but not B: $16 - 9 = 7$.