Question

IfA={x : x=6n, n∈W and n<6}, B={x : x=2n, n ∈N and 2<n≤9} and C={x : x=3n, n ∈N and 4≤n<10} and then show that
A - (B∩C)=(A-B) ∪ (A-C). ( 2 marks)

Answer 1

Solution:

Step 1:

Given,
A = {0, 6, 12, 18, 24, 30};

B = {6, 8, 10, 12, 14, 16, 18}

and C = {12, 15, 18, 21, 24, 27}
B∩C = {6, 8, 10, 12, 14, 16, 18} ∩ {12, 15, 18, 21, 24, 27}
= {12, 18}
A – (B∩C) = {0, 6, 12, 18, 24, 30} – {12, 18}
= {0, 6, 24, 30} ……………………………………(1) (1 mark)

Step 2:
A – B = {0, 6, 12, 18, 24, 30} – {6, 8, 10, 12, 14, 16, 18}
= {0, 24, 30}
A – C = {0, 6, 12, 18, 24, 30} – {12, 15, 18, 21, 24, 27}
= {0, 6, 30}
(A – B) ∪ (A – C) = {0, 24, 30} ∪ {0, 6, 30}
= {0, 6, 24, 30} ……………………………..(2)
From (1) and (2) we get,
A-(B∩C)=(A-B)∪(A-C) ( 1 mark)