NCERT Class XI Mathematics - Mathematical Reasoning - Solutions
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Question : 5
Total: 25
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.
(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.
Solution:
(i) The component statements are:
p : Number 3 is prime
q : Number 3 is odd.
Both the component statements p and q are true.
(ii) The component statements are:
p : All integers are positive.
q : All integers are negative.
Both the component statements p and q are false.
(iii) The component statements are:
p : 100 is divisible by 3.
q : 100 is divisible by 11.
r : 100 is divisible by 5.
The component statements p and q are false whereas r is true.
p : Number 3 is prime
q : Number 3 is odd.
Both the component statements p and q are true.
(ii) The component statements are:
p : All integers are positive.
q : All integers are negative.
Both the component statements p and q are false.
(iii) The component statements are:
p : 100 is divisible by 3.
q : 100 is divisible by 11.
r : 100 is divisible by 5.
The component statements p and q are false whereas r is true.
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