PROPOSITIONAL LOGIC: A. 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. a. r ^ q → p b. p̅ → q c. q → p̅ v r 2. Write T if the above item is true and F if it false. Show solution. (3 pts each) a. b. c B. Show whether or not p ↔ q ≡ (p → q) ^ (q → p) C. 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:
The Answer to the Question
is below this banner.
Here's the Solution to this Question
If a square is a rectangle and a rectangle has 2 parallel sides, then a square had four equal sides.
If a square has four equal sides, then a rectangle has 2 parallel sides.
If a rectangle has 2 parallel sides, then a square has four sides or a square is a rectangle.
2. a. F
C. Using truth table
Hence they are equivalent
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.