Question

Question 3 Find the component statements of the following compound statements and check whether they are true or false.

(i) Number 3 is prime or it is odd.

(ii) All integers are positive or negative.

(iii) 100 is divisible by 3, 11 and 5.

Class X1 - Maths -Mathematical Reasoning Page 329

Answer 1

process : First of all we have to separate the given compound statement into component statements .
After that we have to check whether they are true or false.

(i) Natural 3 is prime or it is odd .
P : number 3 is prime.
Q : number 3 is odd.

we know, 3 is prime as well as odd number .
hence, P, Q are true .

(ii) All integers are positive or negative.
P : all integers are positive.
Q : all integers are negative.
we know, integer is positive as well as negative non fractional number . { or positive and negative Natural number }
hence, both P and Q are false .

(iii) 100 is divisible by 3, 11, 15
P : 100 is divisible by 3
Q : 100 is divisible by 11
R : 100 is divisible by 15

we know, 100 can't be divisible by 3, 11 and 15
hence, P, Q and R are false statements .