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.

hope it you

step-by-step explanation:

sin(7pi/6 - pi/3)  

= sin(7pi/6 - 2pi/6)  

= sin(5pi/6)  

= sin(pi - pi/6)  

= sin(pi/6)  

= 1/2  

sin 7pi/6 - sin pi/3  

= sin (pi + pi/6) - sin pi/3  

= -sin pi/6 - sin pi/3  

= -1/2 - sqrt(3)/2  

= -(1+sqrt(3))2

won't that be plagrisim thought?

step-by-step explanation: