Question

Let A = {x ∈ W | x < 2},
B = {x ∈ N | 1 < 1 < × < 4} and
C = {3,5}. Verify that
(i) A × (B ∪ C) = (A × B) ∪ (A × C)​

Answer 1

Step-by-step explanation:

A={0,1},B={2,3,4} and C={3,5}

∪ is combination of two sets.

B∪C={2,3,4,5}

Now,

L.H.S=A×(B∪C)

={0,1}×(2,3,4,5}

={(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)} ---- ( 1 )

R.H.S=(A×B)∪(A×C)

={0,1}×{2,3,4}∪{0,1}×{3,5}

={(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)}∪{(0,3),(0,5),(1,3),(1,5)}

={(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)} ---- ( 2 )

From ( 1 ) and ( 2 )

⇒ L.H.S=R.H.S

∴ A×(B∪C)=(A×B)∪(A×C)