Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • Write the component statements of the following compound statements and check whether the compound statement is true or false. 57 is divisible by 2 or 3.

Write the component statements of the following compound statements and check whether the compound statement is true or false.
57 is divisible by 2 or 3.

ii) 57 is divisible by 2 or 3.
24 is a multiple of 4 and 6.

iii) 57 is divisible by 2 or 3.
All living things have two eyes and two legs.

iv) 57 is divisible by 2 or 3.
2 is an even number and a prime number.

 

Answers (1)

i) Concept:

A compound statement is defined as a combination of two statements or components. Here the components of the given statement “57 is divisible by 2 or 3”, will be –

p: 57 is divisible by 2 &

q: 57 is divisible by 3

Here, the given statement is true. Compound statement is in the form P V Q, which has truth value T if either P or Q or both will be true.

ii) Concept:

A compound statement is defined as a combination of two statements or components. Here the components of the given statement “24 is a multiple of 4 & 6”, will be –

p: 24 is a multiple of 4 &

q: 24 is a multiple of 6

Here, the given statement is true as both p & q are true since 24 is a multiple of both 4 & 6.

iii) Concept

A statement is considered as an assertive sentence if it is either true or false, but it shouldn’t be both.The given sentence is a true statement, since we know that “All living things have two eyes and two legs”, will be –

p: All living things have two eyes &

q: All living things have two legs.

Compound statement is in the form P\wedge Q, which has truth value T which will be true only if both the components will be true.

Here p is false & q is true. Hence, the given statement is false.

iv) Concept

A compound statement is defined as a combination of two statements or components. Here the components of the given statement “2 is an even number and a prime number”, will be –

p: 2 is an even number &

q: 2 is a prime number.

Compound statement is in the form P ? Q, which has truth value T which will be true only if both the components will be true. Here p & q both are true.

Hence, the given statement is true.

Posted by

infoexpert23

View full answer

Similar Questions

Latest Question