Question

If A = {1,2,3}, B = {2,3,4}, C = {1,3,4} and D = {2, 4, 5}, then verify that (A × B) ∩ (C × D) = (A ∩ C) × (B ∩ D)​

Answer 1

Answer:

A×B is the subset of BxC

Step-by-step explanation:

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11th

Maths

Relations and Functions

Cartesian Product of Sets

Let A = {1, 2}, B = {1, 2, ...

MATHS

Let A={1,2},B={1,2,3,4},C={5,6} and D={5,6,7,8} Verify that

(i) A×(B∩C)=(A×B)∩(A×C)

(ii) A×C is a subset of B×D

EASY

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VIDEO EXPLANATION

ANSWER

(i) To verify : A×(B∩C)=(A×B)∩(A×C)

We have B∩C={1,2,3,4}∩{5,6}=ϕ

∴ L.H.S = A×(B∩C)=A×ϕ=ϕ

A×B={(1,1),(1,2),(1,3),(1,4),(2,1),(2,2),(2,3),(2,4)}

A×C={(1,5),(1,6),(2,5),(2,6)}

∴R.H.S.=(A×B)∩(A×C)=ϕ

∴L.H.S=R.H.S

Hence A×(B∩C)=(A×B)∩(A×C)

(ii) To verify: A×C is a subset of B×D

A×C={(1,5),(1,6),(2,5),(2,6)}

B×D={(1,5),(1,6),(1,7),(1,8),(2,5),(2,6),(2,7),(2,8),(3,5),(3,6),(3,7),

(3,8),(4,5),(4,6),(4,7),(4,8)}

We can observe that all the elements of set A×C are the elements of set B×D

Therefore A×C is a subset of B×D

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