Question

1) Rewrite the following statement in the form of conditional statement.

i) The square of an odd number is odd.

2) Rewrite the following statement in the form of conditional statement.

ii) You will get a sweet dish after the dinner.

3) Rewrite the following statement in the form of conditional statement.

iii) You will fail, if you will not study.

4) Rewrite the following statement in the form of conditional statement.

iv) The unit digit of an integer is $0$ or $5$ if it is divisible by $5$.

5) Rewrite the following statement in the form of conditional statement.

v) The square of a prime number in not prime.

6) Rewrite the following statement in the form of conditional statement.

vi) $2b=a+c,ifa,b\text{and}c\text{are in}A.P.$

Answer 1

1) Given statement: ''The square of an odd number is odd''

Here,

$p:$ The number is odd.

$p:$ The square of an odd number is odd.

$\because$ If $p$ and $q$ are any two statements, then the compound statement ''If $p$ then $q$'' formed by joining $p$ and $q$ by a connective ''if -then'' is called conditional statement.

$\therefore$ Conditional statement of given statement is:

If the number is odd number, then its square is odd number.


2) Given statement: ''You will get a sweet dish after the dinner''

Here,

$p:$ Take the dinner.

$q:$ You will get a sweet dish.

$\because$ If $p$ and $q$ are any two statements, then the compound statement ''If $p$ then $q$'' formed by joining $p$ and $q$ by a connective ''if -then'' is called conditional statement.

$\therefore$ Conditional statement of given statement is:

If you take dinner, then you will get a sweet dish.

3) Given statement: ''You will fail, if you will not study''

Here,

$p:$ You do not study.

$q:$ You will fail.

$\because$ If $p$ and $q$ are any two statements, then the compound statement ''If $p$ then $q$'' formed by joining $p$ and $q$ by a connective ''if -then'' is called conditional statement.

$\therefore$ Conditional statement of given statement is:

If you do not study, then you will fail.

4) Given statement: ''The unit digit of an integer is $0or5\text{if it is divisible by}5$''

Here,

$p:$ An integer is divisible by $5.$

$q:$ Unit digit of an integer is $0or5.$

$\because$ If $p$ and $q$ are any two statements, then the compound statement ''If $p$ then $q$'' formed by joining $p$ and $q$ by a connective ''if -then'' is called conditional statement.

$\therefore$ Conditional statement of given statement is:

If an integer is divisible by $5,$ then its unit digit is $0or5.$

5) Given statement: ''The square of a prime number is not prime''

Here,

$p:$ A number is prime.

$q:$ Square of a number is not prime.

$\because$ If $p$ and $q$ are any two statements, then the compound statement ''If $p$ then $q$'' formed by joining $p$ and $q$ by a connective ''if -then'' is called conditional statement.

$\therefore$ Conditional statement of given statement is:

If a number is prime, then its square is not prime.

6) Given statement: ${}^{\prime \prime }2b=a+c,\text{if}a,b\text{and}c\text{are in}A.P{.}^{\prime \prime }$

Here,

$p:a,b\text{and}c\text{are in}A.P.$

$q:2b=a+c$

$\because$ If $p$ and $q$ are any two statements, then the compound statement ''If $p$ then $q$'' formed by joining $p$ and $q$ by a connective ''if -then'' is called conditional statement.

$\therefore$ Conditional statement of given statement is:

If $a,b\text{and}c\text{are in}A.P.,$ tnen $2b=a+c$