Question

example 1.1 if A { 1,2,5 } AND B = {2,3} THEN 1. SHOW THAT N { A×B} = { B×A } N {B×A} = n (a ) × n (b)
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Answer 1

Answer:

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