Q. 65.0( 1 Vote )

Write down the negation of following compound statements

(i) All rational numbers are real and complex.

(ii) All real numbers are rationals or irrationals.

(iii) x = 2 and x = 3 are roots of the Quadratic equation x2 – 5x + 6 = 0.

(iv) A triangle has either 3-sides or 4-sides.

(v) 35 is a prime number or a composite number.

(vi) All prime integers are either even or odd.

(vii) |x| is equal to either x or – x.

(viii) 6 is divisible by 2 and 3.

Answer :

(i) The given statement is compound statement then components are,

P:All rational numbers are real.


~p: All rational numbers are not real.


q: All rational numbers are complex.


~q: All rational numbers are not complex.


(p q)= All rational numbers are real and complex.


~(p q)=~p v ~q= All rational numbers are neither real nor complex.


(ii) The given statement is compound statement then components are,


P:All real numbers are rational.


~p: All real numbers are not rational.


q: All real numbers are irrational.


~q: All real numbers are not irrational.


(p q)= All real numbers are rationals or irrationals.


~(p q)=~p v ~q= All real numbers are neither rationals nor irrationals.


(iii) The given sentence is a compound statement in which components are


p: x = 2 is a root of Quadratic equation x2 – 5x + 6 = 0.


~p: x = 2 is not a root of Quadratic equation x2 – 5x + 6 = 0.


q: x = 3 is a root of Quadratic equation x2 – 5x + 6 = 0.


~q: x = 3 is not a root of Quadratic equation x2 – 5x + 6 = 0.


(p q)= x = 2 and x = 3 are roots of the Quadratic equation x2 – 5x + 6 = 0.


~(p q)=~p v ~q= Neither x = 2 and nor x = 3 are roots of x2 – 5x + 6 = 0


(iv) The given statement is compound statement then components are,


P:A triangle has 3 sides


~p: A triangle does not have 3 sides.


q: A triangle has 4 sides.


~q: A triangle does not have 4 side.


(p v q)= A triangle has either 3-sides or 4-sides.


~(p v q)=~p ~q= A triangle has neither 3 sides nor 4 sides.


(v) The given statement is compound statement then components are,


P: 35 is a prime number


~p: 35 is not a prime number.


q: 35 is a composite number


~q: 35 is not a composite number.


(p v q)= 35 is a prime number or a composite number.


~(p v q)=~p ~q= 35 is not a prime number and it is not a composite number.


(vi) The given statement is compound statement then components are,


P: All prime integers are even


~p: All prime integers are not even.


q: All prime integers are odd


~q: All prime integers are not odd.


(p v q)= All prime integers are either even or odd.


~(p v q)=~p ~q= All prime integers are not even and not odd.


(vii) The given statement is compound statement then components are,


P: |x| is equal to x.


~p: |x| is not equal to x.


q: |x| is equal to –x.


~q: |x| is not equal to -x.


(p v q)= |x| is equal to either x or – x.


~(p v q)=~p ~q= |x| is not equal to x and |x| is not equal to – x.


(viii) The given statement is compound statement then components are,


P: 6 is divisible by 2


~p: 6 is not divisible by 2


q: 6 is divisible by 3


~q: 6 is not divisible by 3.


(p q)= 6 is divisible by 2 and 3.


~(p q)=~p v ~q= 6 is neither divisible by 2 nor 3


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Scalar and Vector Product49 mins
Addition of Vectors - Kick start Your Preparations47 mins
Take the challenge, Quiz on Vectors37 mins
Vectors- Cosine & SIne Rule54 mins
Interactive Quiz on vector addition and multiplications38 mins
Scalar and vector product in one shot56 mins
Revise Complete Vectors & it's application in 50 Minutes51 mins
Unit Vectors24 mins
Quick Revision of Vector Addition and MultiplicationsFREE Class
Quiz | Vector Addition and MultiplicationsFREE Class
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses
RELATED QUESTIONS :