Prove each statement that is true and find a counterexample for each statement that is false. assume all sets are subsets of a universal set u.
for or all sets a, b, and c, a∩(b−c) = (a∩ b)−(a∩c)
hint: the statement is true. sketch of proof: if x ∈ a∩(b−c), then x∈a and x∈b and x∉c. so it is true that x∈a and x∈b and that x∈a and x∉c. conversely, if x ∈ (a∩ b)−(a∩c), then x∈a and x∈b, but x ∉ a∩c, and so x∉c.

Answer with Step-by-step explanation:

We are given that A, B and C are subsets of universal set U.

We have to prove that

Proof:

Let x

Then and

When then but

Therefore, but

Hence, it is true.

Conversely , Let but

Then and

When then

Therefor,

Hence, the statement is true.

h * s * a

h = history teacher

s = science teacher

a =   art teacher.

i see no data table, but just multiply the number of history teachers, science teachers, and art teachers.