Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main
Exam
JEE Main
Subject
Mathematics
Chapter
Sets and Relations

JEE Main · Mathematics · Sets and Relations

For two sets A and B , if n(A) = 7, n(B) = 13 and n(A B) = 5 , then...

For two sets AA and BB, if n(A)=7,n(B)=13\text{n}\left(\text{A}\right) = 7, \text{n}\left(\text{B}\right) = 13 and n(A∩B)=5\text{n}\left(\text{A} \cap \text{B}\right) = 5, then the incorrect statement is

Options

  1. An(A∪B)=15n\left(A \cup B\right) = 15
  2. Bn(A−B)=6n\left(A - B\right) = 6
  3. Cn(A×B)=91n\left(A \times B\right) = 91
  4. Dn{(A∪B)×(A⋂B)}=75n\left\{\left(A \cup B\right) \times \left(A ⋂ B\right)\right\} = 75

Correct answer

B. n(A−B)=6n\left(A - B\right) = 6

Step-by-step solution

∵n(A)=7,n(B)=13∵ n\left(A\right) = 7, n\left(B\right) = 13
∵n(A−B)=n(A)−n(A∩B)=7−5=2∵ \text{n}\left(\text{A} - \text{B}\right) = \text{n}\left(\text{A}\right) - \text{n}\left(\text{A} \cap \text{B}\right) = 7 - 5 = 2
n \left(A \cup B\right) = n \left(A\right) + n\left(B\right) - n\left(A \cap B\right)<br/><br/>= 7 + 13 - 5 = 15<br/><br/>n \left(A \timesB\right) = n \left(A\right)\timesn(B)\timesn \left(B\right)
7×13=917 \times13 = 91
n{(A∪B)×(A∩B)}\text{n} \left\{\left(\text{A}\cup \text{B}\right) \times \left(\text{A}\cap \text{B}\right)\right\} = 15 ×\times5 = 75
Practice Sets and Relations on Quantrex Academy →

More from Sets and Relations

Let S = \ 1, 2, 3, …, 10\ . Consider the set X = \ R : R is an equivalence relation on… JEE Advanced 2026Consider the relation R on the set \ -2,-1,0,1,2\ defined by (a, b) ∈ R if and only if… JEE Main 2026Let R = \ (x, y) ∈ ℕ × ℕ : _e(x + y) ≤ 2\ . Then the minimum number of elements, required… JEE Main 2026Let A = \ 1, 4, 7\ and B = \ 2, 3, 8\ . Then the number of elements, in the relation R =… JEE Main 2026Let A = \ 2, 3, 4, 5, 6\ . Let R be a relation on the set A × A given by (x, y) R (z, w)… JEE Main 2026Let R be a relation defined on the set \ 1,2,3,4\ ×\ 1,2,3,4\ by R=\ ((a, b),(c, d)): 2… JEE Main 2026Let A=\ 0,1,2, …, 9\ . Let R be a relation on A defined by (x, y) ∈ R if and only if… JEE Main 2026Let A=\ -2,-1,0,1,2,3,4\ . Let R be a relation on A defined by x Ry if and only if 2 x+y… JEE Main 2026The number of elements in the relation R=\ (x, y): 4 x^ 2 +y^ 2 <52, x, y ∈ Z\ is JEE Main 2026Let S be the set of the first 11 natural numbers. Then the number of elements in A=\ B ⊆… JEE Main 2026Let the relation R on the set M=\ 1,2,3, …, 16\ be given by R=\ (x, y): 4 y=5 x-3, x, y ∈… JEE Main 2026Let A=\ x:|x^ 2 -10| ≤ 6\ and B=\ x:|x-2|>1\ . Then JEE Main 2026Let A=\ 2,3,5,7,9\ . Let R be the relation on A defined by x R y if and only if 2 x ≤ 3 y… JEE Main 2026The number of relations, defined on the set \ a, b, c, d\ , which are both reflexive and… JEE Main 2026Let the set of all relations R on the set \ a, b, c, d, e, f\ , such that R is reflexive… JEE Advanced 2025Let A=\ 0,1,2,3,4,5\ . Let R be a relation on A defined by (x, y) ∈ R if and only if max… JEE Main 2025 Full Sets and Relations list Sets and Relations JEE Maths PYQsJEE Mathematics PYQs All 99 Percentile Qs Bank for JEE Main PYQs