For two sets $A$ and $B$ , let $A \Delta B$ denote the set of elements which belong to $A$ or $B$ but not both. If $P=\{1,2,3,4\}, Q=\{2,3,5,6\},, R=\{1,3,7,8,9\}, S=$ $\{2,4,9,10\}$ , then the number of elements in $(P \Delta Q) \Delta(R \Delta S)$ is

$7$

$6$

$8$

$9$

✅ Correct Option: 1

The symmetric difference A Δ B is the set of elements that belong to either A or B, but not both.

Think of it as "everything that's different between the two sets."

Example: If A = {1, 2, 3} and B = {2, 3, 4}, then A Δ B = {1, 4}

1 is in A but not in B

4 is in B but not in A

2 and 3 are in both sets, so they're excluded

Given: P = {1, 2, 3, 4} and Q = {2, 3, 5, 6}

Elements in P but not in Q: 1, 4

Elements in Q but not in P: 5, 6

Therefore: P Δ Q = {1, 4, 5, 6}

Given: R = {1, 3, 7, 8, 9} and S = {2, 4, 9, 10}

Elements in R but not in S: 1, 3, 7, 8

Elements in S but not in R: 2, 4, 10

Therefore: R Δ S = {1, 2, 3, 4, 7, 8, 10}

Now we find the symmetric difference between our two results:

P Δ Q = {1, 4, 5, 6}

R Δ S = {1, 2, 3, 4, 7, 8, 10}

Elements in (P Δ Q) but not in (R Δ S): 5, 6

Elements in (R Δ S) but not in (P Δ Q): 2, 3, 7, 8, 10

Therefore: (P Δ Q) Δ (R Δ S) = {2, 3, 5, 6, 7, 8, 10}

The number of elements in (P Δ Q) Δ (R Δ S) is 7.

When working with symmetric difference, we always remember that we're looking for elements that appear in one set but not the other. Elements that appear in both sets get "cancelled out"!

2025 Slot 3

In a class of 150 students, 75 students chose physics, 111 students chose mathematics and 40 students chose chemistry. All students chose at least one of the three subjects and at least one student chose all three subjects. The number of students who chose both physics and chemistry is equal to the number of students who chose both chemistry and mathematics, and this is half the number of students who chose both physics and mathematics. The maximum possible number of students who chose physics but not mathematics, is

CAT 2018 Slot 2

If $A=\left\{6^{2 n}-35 n-1: n=1,2,3, \ldots\right\}$ and $B=\{35(n-1): n=1,2,3, \ldots\}$ then which of the following is true?

CAT 2022 Slot 1

In a class of $100$ students, $73$ like coffee, $80$ like tea and $52$ like lemonade. It may be possible that some students do not like any of these three drinks. Then the difference between the maximum and minimum possible number of students who like all the three drinks is

CAT 2018 Slot 1

If among $200$ students, $105$ like pizza and $134$ like burger, then the number of students who like only burger can possibly be

CAT 2024 Slot 3

In a group of $250$ students, the percentage of girls was at least $44\%$ and at most $60\%$ . The rest of the students were boys. Each student opted for either swimming or running or both. If $50\%$ of the boys and $80\%$ of the girls opted for swimming while $70\%$ of the boys and $60\%$ of the girls opted for running, then the minimum and maximum possible number of students who opted for both swimming and running, are

CAT 2018 Slot 1

Each of $74$ students in a class studies at least one of the three subjects $H, E$ and $P$ . Ten students study all three subjects, while twenty study $H$ and $E$ , but not $P$ . Every student who studies $P$ also studies $H$ or $E$ or both. If the number of students studying $H$ equals that studying $E$ , then the number of students studying $H$ is

Solution

Related questions:

Keyboard Shortcuts

CAT Past Year Questions (Topic-Wise)