Determine the truth value of the following statement. It is not true that 5 + 5 = 9 or Earth is a planet - Mathematics

Determine the truth value of the following statement.

It is not true that 5 + 5 = 9 or Earth is a planet

Sum

p: 5 + 5 = 9 (F)

q: Earth is a planet (T)

∴ ¬p v q is having the truth value T

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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 3. (iii) | 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 → ¬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 following sentences in symbolic form using statement variables p and q.

19 is not a prime number

Which one of the following sentences is a proposition?

What are you doing?

Which one of the following sentences is a proposition?

How tall this mountain is!

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

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

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

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

(p → q) ↔ (¬p → q)

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

((p → q) ∧ (q → r)) → (p → r)

Show that ¬(p ↔ q) ≡ p ↔ ¬q

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