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.

the answer is (4,3)

since the rule for r0, 90º is (-y,x) and it was already applied to form the image, all you have to do is reverse the answer using this formula.

distance covered by pamela in 9 l of fuel = 99km

let us apply unitary method here.

distance covered by pamela in 1 l of fuel =99/9 =11 km

now let us find distance covered by pamela if she has 12 l of fuel.

distance covered in 12 l = distance covered in 1 l of fuel * 12

we know that distance covered by here in 1 l is 11 km.

so distance covered in 12 l of fuel = 11*12 = 132 km.