For each of 1-4 find a counterexample to show that the statement is false. Assume all sets are subsets of a universal set U.
For all sets A,B, and C, if B ∪ C ⊆ A then
( A − B ) ∩ ( A − C ) = ∅ .

For all sets A,B and C, if B∩C⊆A then

(A−B)∩(A−C)=ϕ.

Given information:

Let  A,B and C   be any set

Concept used:

∪:Union of sets∩:Intersection of sets

⊆: subset of set

Calculation:

For each find a counterexample to show that the statement ¡s false. Assume all sets are subsets of a universal set U.

Exercise

For all sets A,B and C, if B∩C⊆A then

(A−B)∩(A−C)=ϕ.

Consider the statement as.

“For all sets A,B and C, if B∩C⊆A then (A−B)∩(A−C)=ϕ ”.

The objective is to find a counter example to show that the above statement is false.

Consider that all sets are subsets of a universal set U.

Counterexample:

Let U be a universal set defined as,

U={1,2,3,4,5,6}.

Suppose for some sets A and B defined as,

A={1,4}, B={1,2,3} and C={1,5,6}.

B∩C={1,2,3}∩{1,5,6}={1}⊂A