Question

Find the component statements for the following given statements and check whether it is true or false:
(a) A square is a quadrilateral and its four sides are equal
(b) All prime numbers are either even or odd
​

Answer 1

━━━━━━━━━━━━━━━━━━━━━━

━━━

$\Large\fbox{\color{purple}{QUESTION}}$

Find the component statements for the following given statements and check whether it is true or false:

(a) A square is a quadrilateral and its four sides are equal

(b) All prime numbers are either even or odd

━━━━━━━━━━━━━━━━━━━━━━━━━

$\Large\fbox{\color{purple}{ SOLUTION }}$

━━━━━━━━━━━━━━━━━━━━━━━━━

✴➡️(a) Given statement: A square is a quadrilateral and its four sides are equal

➡️The component statements are:

➡️P: A square is a quadrilateral

➡️Q: A square has all its sides equal.

➡️In this statement, the connecting word is “and”

We know that a square is a quadrilateral

➡️So, the statement P is true.

➡️Also, it is known that all the four sides of a

square are equal.

➡️Hence, the statement “Q” is also true.

➡️Therefore, both the component statements are true.

✴➡️(b) Given statement: All prime numbers are either even or odd

➡️The component statements are:

➡️P: All the prime numbers are odd numbers

➡️Q: All the prime numbers are even numbers

➡️In this statement, the connecting word is “or”

We know that all the prime numbers are not odd numbers

➡️So, the statement P is false.

➡️Also, it is known that all the prime numbers are not even numbers.

➡️Hence, the statement “Q” is also false.

➡️Therefore, both the component statements are not true.

$\Large\mathcal\green{FOLLOW \: ME}$

━━━━━━━━━━━━━━━━━━━━━━━━━

Answer 2

Answer:

SOLUTION:-

⭐➡️(a) Given statement:

A square is a quadrilateral and its four sides are equal

➡️The component statements are:

➡️P: A square is a quadrilateral

➡️Q: A square has all its sides equal.

➡️In this statement, the connecting word is “and”

We know that a square is a quadrilateral

➡️So, the statement P is true.

➡️Also, it is known that all the four sides of a

square are equal.

➡️Hence, the statement “Q” is also true.

➡️Therefore, both the component statements are true.✔✔

-------------------------------------------

⭐➡️(b) Given statement: All prime numbers are either even or odd

➡️The component statements are:

➡️P: All the prime numbers are odd numbers

➡️Q: All the prime numbers are even numbers

➡️In this statement, the connecting word is “or”

We know that all the prime numbers are not odd numbers

➡️So, the statement P is false.

➡️Also, it is known that all the prime numbers are not even numbers.

➡️Hence, the statement “Q” is also false.

➡️Therefore, both the component statements are not true.✔✔

Explanation:

HOPE IT HELP YOU ✌✌