Question

3.If  A={x:0≤x≤5}; B={x:2≤x≤4}; C= {x:1≤ x ≤ 5} and D ={x:5≤x ≤7} then find a) A Δ B b) B U C c) A – B d) C –D.​

Answer 1

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×