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.
A compound statement is made up of two or more statements and each statement in the compound statement is known as component statement.
(i)
The given compound statement is: Number 3 is prime or it is odd where or is the word which joins two statements. The component statements of the given compound statement are:
A: Number 3 is prime.
B: Number 3 is odd.
Since 3 is a prime number and also it is an odd number, thus both the component statements are true.
(ii)
The given compound statement is: All integers are positive or negative where or is the word which joins two statements. The component statements of the given compound statement are:
A: All integers are positive.
B: All integers are negative.
Since integers can be either positive or negative but in the statement it is given that all integers are positive and the same is for negative, thus both the component statements are false.
(iii)
The given compound statement is: 100 is divisible by 3, 11 and 5 where the word “and” and comma joins three statements. The component statements of the given compound statement are:
A: 100 is divisible by 3.
B: 100 is divisible by 11.
C: 100 is divisible by 5.
Since 100 is neither divisible by 3 nor by 11, therefore the statements A and B are false but 100 is divisible by 5, thus the statement C is true.
A compound statement is made up of two or more statements and each statement in the compound statement is known as component statement.
(i)
The given compound statement is: Number 3 is prime or it is odd where or is the word which joins two statements. The component statements of the given compound statement are:
A: Number 3 is prime.
B: Number 3 is odd.
Since 3 is a prime number and also it is an odd number, thus both the component statements are true.
(ii)
The given compound statement is: All integers are positive or negative where or is the word which joins two statements. The component statements of the given compound statement are:
A: All integers are positive.
B: All integers are negative.
Since integers can be either positive or negative but in the statement it is given that all integers are positive and the same is for negative, thus both the component statements are false.
(iii)
The given compound statement is: 100 is divisible by 3, 11 and 5 where the word “and” and comma joins three statements. The component statements of the given compound statement are:
A: 100 is divisible by 3.
B: 100 is divisible by 11.
C: 100 is divisible by 5.
Since 100 is neither divisible by 3 nor by 11, therefore the statements A and B are false but 100 is divisible by 5, thus the statement C is true.
