Rewrite each of the following statements in the form of conditional statements
(i) The square of an odd number is odd.
(ii) You will get a sweet dish after the dinner.
(iii) You will fail, if you will not study.
(iv) The unit digit of an integer is 0 or 5 if it is divisible by 5.
(v) The square of a prime number is not prime.
(vi) 2b = a + c, if a, b and c are in A.P.
(i) The square of an odd number is odd.
In the conditional statement, expression is
If p, then q
Now,
The given statement p and q are
p: The number is odd.
q: The square of odd number is odd.
Therefore,
If the number is odd, then its square is odd number.
(ii) You will get a sweet dish after the dinner.
In the conditional statement, expression is
If p, then q
Now,
The given statement p and q are
p: Take the dinner
q: you will get sweet dish
Therefore,
If take the dinner, then you will get sweet dish.
(iii) You will fail, if you will not study.
In the conditional statement, expression is
If p, then q
Now,
The given statement p and q are
p: You do not study
q: you will fail.
Therefore,
If you do not study, then you will fail.”
(iv) The unit digit of an integer is 0 or 5 if it is divisible by 5.
In the conditional statement, expression is
If p, then q
Now,
In the given statement p and q are
p: An integer is divisible by 5
q: Unit digits of an integer are 0 or 5
Therefore,
If an integer is divisible by 5, then its unit digits are 0 or 5.
(v) The square of a prime number is not prime.
In the conditional statement, expression is
If p, then q
Now,
The given statement p and q are
p: Any number is prime,
q: square of number is not prime.
Therefore,
If any number is prime, then its square is not prime”.
(vi) 2b = a + c, if a, b and c are in A.P.
In the conditional statement, expression is
If p, then q
Now,
The given statement p and q are
p: a, b and c are in AP
q: 2b=a + c
Therefore,
If a, b, c are in AP then 2b=a + c.