Answer to Question #208703 in Discrete Mathematics for Muhannedo

Question

1. What are the converse, inverse and contrapositive of the statement

“If you try hard, then you will win”

Converse

Inverse

Contrapositive

b. Determine whether this proposition is a tautology, contradiction or contingency using the truth table: (p  q)  (q →  rp)  (p  r)

Question 4

a. Write the set S= {1, 3, 5, 7} in set builder notation.

b. Write the set T={ x | x ∈ R, x2 = 9 or x2 = 64} in a list form.

c. Let A = {x, y, z }and B = {2, 5, 6}

List the elements of the following sets.

i. Power(B ) =

ii. B  A =

d. What are the truth sets of the predicates P(x), Q(x), and R(x), where the domain is the set of integers and

1. P(x) is “|x| = 4,”

2. Q(x) is “x2 = 16,”

3. R(x) is “|x| = x”

Question 5:

Given the below premises Prove: B.

1.  (A v B) → C 2. A

3. C