If the two sets A and B are having 43 elements in common, then the number of elements common to each of the se

Miscellaneous Exercise 5 (I) · Q85

Q. If the two sets A and B are having 43 elements in common, then the number of elements common to each of the sets A \times B and B \times A is: A) 43² B) 2^43 C) 43^43 D) 2^86

Maharashtra MsbshseTextbookSubjectiveImportance★★★★★

73% · 85/117 Questions

🔒 Locked · start free trial →

You're viewing a preview — the full solution, concept, methods & PYQ mapping are locked.

Start your 14-day free trial to unlock the full solution →

An ordered pair $(x,y)$ lies in BOTH $A\times B$ and $B\times A$ exactly when $x\in A, y\in B$ (for it to be in $A\times B$ ) AND $x\in B, y\in A$ (for it to be in $B\times A$ ) — together this forces $x\in A\cap B$ and $y\in A\cap B$ . Since $n(A\cap …

Start your 14-day free trial to unlock the full solution →

Same / Similar Concept — real previous-year questions on the same or a closely similar concept, not this exact question.

CA Foundation 2026Set jan-20261 markMCQ
$A=\{2,\ 3\}$
›Reveal solutionSolution

$B\cap C=\{5\}$ , so $A\times\{5\}=\{(2,5),(3,5)\}$ .

Step 1 — Intersection $B\cap C$

Keep only the elements common to both sets:
$B\cap C=\{4,5\}\cap\{5,6\}=\{5\}.$
Step 2 — Cartesian product $A\times(B\cap C)$

Pair each element of $A=\{2,3\}$ with each element of $\{5\}$ , writing each ordered pair as (element from $A$ , element from $B\cap C$ ):

$A\times\{5\}=\{(2,5),\ (3,5)\}.$ …
Start your 14-day free trial to see the full solution →
CA Foundation 2025Set jan-20251 markMCQ
$A = \{a, b, p\}$
›Reveal solutionSolution

$n(A \cup C) = 6$ , $n(B) = 2$ , so $n[(A \cup C) \times B] = 6 \times 2 = 12$ .

Step 1 — Form the union
$A \cup C = \{a, b, p\} \cup \{p, q, r, s\} = \{a, b, p, q, r, s\}$
The element $p$ is common and counted only once, so $n(A \cup C) = 6$ .

Step 2 — Note the size of $B$
$B = \{2, 3\} \;\Rightarrow\; n(B) = 2$
Step 3 — Cardinality of the Cartesian product
$n(X \times Y) = n(X) \times n(Y) = 6 \times 2 = 12$
Start your 14-day free trial to see the full solution →
CA Foundation 2023Set jun-20231 markMCQ
$A=\{a, b, c\}, B=\{b, c, d\}$
›Reveal solutionSolution

A − B = {a}, B ∩ C = {c, d}, so {a} × {c, d} = {(a, c), (a, d)}.

Step 1 — Set difference

A = {a, b, c}, B = {b, c, d}: elements of A not in B ⇒ A − B = {a}.

Step 2 — Intersection

B = {b, c, d}, C = {a, d, c}: common elements ⇒ B ∩ C = {c, d}.

Step 3 — Cartesian product
$\{a\} \times \{c, d\} = \{(a, c), (a, d)\}$
Watch out

Ordered pairs: the first coordinate must come from A − B, so (c, a) and (d, a) are wrong. …

Start your 14-day free trial to see the full solution →

←Previous questionQ84 — In a city 20% of the population travels by car, 50% travels by bus and…→Next questionQ86 — Let R be a relation on the set N be defined by (x, y) / x, y∈ N, 2x + …

Q.If the two sets A and B are having 43 elements in common, then the number of elements common to each of the sets A × B and B × A is: A) 43² B) 2^43 C) 43^43 D) 2^86

Concept understanding — Cartesian Product of Sets

Step 1 — Intersection $B\cap C$

Step 2 — Cartesian product $A\times(B\cap C)$

Step 1 — Form the union

Step 2 — Note the size of $B$

Step 3 — Cardinality of the Cartesian product

Step 1 — Set difference

Step 2 — Intersection

Step 3 — Cartesian product

Q.If the two sets A and B are having 43 elements in common, then the number of elements common to each of the sets A × B and B × A is: A) 43² B) 2^43 C) 43^43 D) 2^86

🎓Unlock everything free for 14 days

Unlock everything free for 14 days