Question

Let$\mathrm{p}\left(\mathrm{x}\right)$be the statement “the wordcontains the letter” what are these truth values?

(a)p(orange)

(b) p(lemon)

(c) p(true)

(d) p(false)

Short answer

The truth values of p(orange),p(lemon),p(true)and p(false) are true, false, false, and true respectively. For this, check the presence of letter a in a given words and determine the truth values based on this.

Step-by-step solution

Definition of the truth value  

A truth valuein a truth table indicates the truth (Tor1) or falsity (For0) of a specified proposition or statement.

To find the truth values of given propositions.

(a)p (orange)

The given condition is “the wordxcontains the lettera” .

The given proposition isp(orange).

Here, the word orange contains lettera.

Therefore, the statementp(orange)is true.

(b)p (lemon)

The given condition is “the wordxcontains the lettera” .

The given proposition isp(lemon).

Here, the word lemon does not contain lettera.

Therefore, the statementp(lemon)is false.

(c)p (true)

The given condition is “the wordxcontains the lettera” .

The given proposition isp(true).

Here, the word true does not contain lettera.

Therefore, the statementp(true)is false.

(d)p (false)

The given condition is “the word xcontains the letter a” .

The given proposition is p(false) .

Here, the word false contains letter a.

Therefore, the statementp(false)is true.

The truth values ofp(orange),p(lemon),p(true)and p(false) are true, false, false, and true respectively.