Question

write the following statement in symbolic form ,3 is a prime number and 4 is a rational number​

Answer 1

Answer:

3 is a prime number  - Correct  - 1

4 is a rational number - Correct  1

1  and 1  =  1

3 is a prime number and 4 is a rational number - Truth Value is  1

( as both statements are Correct)

Step-by-step explanation:

Answer 2

Complete Question: Write the following statement in symbolic form: 3 is a prime number and 4 is a rational number​. Also write the truth value of the given statement.

Answer: The symbolic form of the statement is p∧q and the truth value of the given statement is 'T'.

Explanation:

→ Assume:

p = 3 is a prime number.

q = 4 is a rational number.

→ Hence the symbolic form of the statement: 3 is a prime number and 4 is a rational number would be p∧q.

As we know that 3 is a prime number, therefore the statement 'p' is true. So the truth value of the statement 'p' would be 'T'.

Also, 4 is a rational number, hence the statement 'q' is also true. So the truth value of the statement 'q' would be 'T'.

→ In case of a compound statement joined by the 'AND' connective:

• If all the component statements connected by the 'AND' connective are True, then the entire compound statement is also True.

• If any one of the component statements connected by the 'AND' connective is false, then the entire compound statement is false.

→ Therefore the truth value of the statement: 3 is a prime number and 4 is a rational number is given as:

                                             p∧q ≡ T∧T ≡ T

→ Hence the truth value of the given statement comes out to be equal to 'T'

Therefore the symbolic form of the given statement is p∧q. The truth value of the given statement is T.

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