I need the following multiple choice assignment Suppose you

I need the following multiple choice assignment:

Suppose you wish to prove a (ES P(x)). The structure of the proof should be (A) Suppose a E S and show that P(x) is true. (B) Suppose a E S and show that P(a) is true. (C) Verify that a E S and show that P(z) is true. (D) Verify that a E S and show that P(a) is true Suppose you wish to prove A C B by direct proof. The structure of the proof should be (A) Suppose a E A and deduce that a B (B) Suppose a A and deduce that a E B (C) Suppose a A and deduce that a B (D) Suppose a B and deduce that a ¢ A. Suppose you wish to prove ACBby contrapositive proof. The structure of the proof should (A) Suppose a A and deduce that a B (B) Suppose a E A and deduce that a EB (C) Suppose a A and deduce that a B (D) Suppose a ¢ B and deduce that a A Consider the statement Suppose you are trying to prove this statement by direct proof. The structure of the proof should be (A) Suppose a E 12n : nEZ) and deduce that a 2n :nE Z) (B) Display an element a such that a {12n ne Z} and deduce that a {2n : nEZy (C) Display an element a such that a {12n : nE Z} and a {2n : nE Z) (D) Suppose a {2n : n Z) and deduce that a ¢ { 12n : n 2)

Solution

1)
Here a belongs to S where as x also belongs to S.
So, this equation shows that p(a) is true.
So correct answer is (A)

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2)
If A is subset of B, then it represents that elements in A are in B.
So, option (B) is correct.

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3)
As discussed ub above answer, the contrapositive statement prrof will belongs
option (A) is correct.

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4)
{12n:n e Z} subset of {2n:n e Z}
So values {12n:n} are belongs to {2n:n}
So correct option is (C)

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5) contrapositive statement will be
correct option is (B)

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6) Inverted \'U\' resembles and condition.
So correct option will be (A)

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7)
contrapositive statement of AND will be OR.
So correct option will be (B)

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8)
Correct option is (D), which is x belongs to (BUD)

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9)
case(1) talks about (AUC), so correct option os (B)

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10)
case1 belongs to (AUC) and case2 belongs to (BUD)
So , x belongs to B and x belongs to D
So correct option is (B)