Answer to Question #180872 in Discrete Mathematics for Angelie Suarez

Question

B.Let p, q and r denotes the following statements:

p: A square has four equal side

q: Rectangle has 2 parallel sides

r: A square is a rectangle. 

1. Express each of the following into English sentence. (3 pts each)

a. r ^ q → p

b. p

̅ → q

c. q → p

̅ v r

2. Write T if the above item is true and F if it false. Show solution. (3 pts

each)

a.

b.

c.

C. Show whether or not p ↔ q ≡ (p → q) ^ (q → p) (8 pts)

D. Find the converse, inverse and contrapositive of the implication: “If today is

Monday then, I have an exam today.” (3 pts each)

1. Inverse:

2. Converse:

3. Contrapositive: 

Answer 1

1. a

$r\wedge q \to p$

If a square is a rectangle and a rectangle has 2 parallel sides, then a square had four equal sides.

b. $p\to q$

If a square has four equal sides, then a rectangle has 2 parallel sides.

c. $(q \to p)\vee r$

If a rectangle has 2 parallel sides, then a square has four sides or a square is a rectangle.

2. a. F

b. T

c. T

C. Using truth table

Hence they are equivalent

D.

Inverse: If today is not Monday, then I have no exam today.

Converse: If I have an exam today, then today is Monday.

Contrapositive: If I have no exam today, then today is not Monday.