If $A \times B = \{(1,x), (1,y), (2,x), (2,y), (3,x), (3,y)\}$, find the sets $A$ and $B$.

If A × B = \(1,x), (1,y), (2,x), (2,y), (3,x), (3,y)\, find the sets A and B.

Exercise: Cartesian Product · Q11

A \times B = \{(1,x), (1,y), (2,x), (2,y), (3,x), (3,y)\}

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Step 1: In $A\times B$ , every ordered pair has its first component from $A$ and second component from $B$ .

Step 2: The distinct first components appearing are $1,2,3$ , so $A=\{1,2,3\}$ . …

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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 $B\cap C$ ):

$A\times\{5\}=\{(2,5),\ (3,5)\}.$ …
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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
$n(X \times Y) = n(X) \times n(Y) = 6 \times 2 = 12$
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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. …

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←Previous questionQ10 — If n(A) = 5 and n(B) = 3, find n(A × B) and n(B × A).→Next questionQ12 — If A = \x : x ∈ mathbbN,x < 3\, find A × A × A and the number of eleme…

Q.If $A \times B = \{(1,x), (1,y), (2,x), (2,y), (3,x), (3,y)\}$ , find the sets $A$ and $B$ .

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 A×B={(1,x),(1,y),(2,x),(2,y),(3,x),(3,y)}A \times B = \{(1,x), (1,y), (2,x), (2,y), (3,x), (3,y)\}A×B={(1,x),(1,y),(2,x),(2,y),(3,x),(3,y)}, find the sets AAA and BBB.

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Q.If $A \times B = \{(1,x), (1,y), (2,x), (2,y), (3,x), (3,y)\}$ , find the sets $A$ and $B$ .

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