Let p : Jupiter is a planet and q : India is an island be any two simple statements. Give verbal sentence describing the following statement. ¬ P

Let p : Jupiter is a planet and q : India is an island be any two simple statements. Give verbal sentence describing the following statement.

¬ P

Sum

p: Jupiter is a planet

q: India is an island

¬ P: Jupiter is not a planet

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Mathematical Logic

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Chapter 12: Discrete Mathematics - Exercise 12.2 [Page 248]

Chapter 12 Discrete Mathematics
Exercise 12.2 | Q 1. (i) | Page 248

Let p : Jupiter is a planet and q : India is an island be any two simple statements. Give verbal sentence describing the following statement.

¬p v q

Write the following sentences in symbolic form using statement variables p and q.

19 is not a prime number and all the angles of a triangle are equal

Write the converse, inverse, and contrapositive of the following implication.

If x and y are numbers such that x = y, then x² = y²

Write the converse, inverse, and contrapositive of the following implication.

If a quadrilateral is a square then it is a rectangle

Construct the truth table for the following statement.

¬P ∧ ¬q

Construct the truth table for the following statement.

(p v q) v ¬q

Verify whether the following compound propositions are tautologies or contradictions or contingency.

((p v q) ∧¬p) → q

Show that p → q and q → p are not equivalent

Using the truth table check whether the statements ¬(p v q) v (¬p ∧ q) and ¬p are logically equivalent

Prove that p → (¬q v r) ≡ ¬p v (¬q v r) using truth table