Question

The statement “ $ x > 5 $ or $ x < 3 $ ” is true, if x equals
A. 1
B. 3
C. 4
D. 5

Answer 1

Hint: Divide the given statement into two and label the parts as p, q. Let $ x > 5 $ be p and $ x < 3 $ be q. Then the statement “ $ x > 5 $ or $ x < 3 $ ” can be logically represented as $ p\;or\;q,p \vee q $ . In logical or, if at least one of the inputs is true then the output is true. So if either $ x > 5 $ or $ x < 3 $ is true then the whole statement is true. Use this info to further find the value of x.

Complete step-by-step answer:
We are given to find the value of x if the statement “ $ x > 5 $ or $ x < 3 $ ” is true.
The statement has a connector “or”. In logical or, if at least one of the inputs is true then the whole output is true.
So if we have to choose x in such a way that either $ x > 5 $ or $ x < 3 $ is true.
Second option is 3. When x is 3 $ x > 5 $ is false and $ x < 3 $ is false.
Third option is 4. When x is 4 $ x > 5 $ is false and $ x < 3 $ is false.
Fourth option is 5. When x is 5 $ x > 5 $ is false and $ x < 3 $ is false.
First option is 1. When x is 1 $ x > 5 $ is false and $ x < 3 $ is true as 1 is less than 3. So here $ x < 3 $ is true therefore the whole statement “ $ x > 5 $ or $ x < 3 $ ” is true.
Hence, the correct option is Option A, when x is equal to 1 “ $ x > 5 $ or $ x < 3 $ ” is true.
So, the correct answer is “Option C”.

Note: Do not confuse between a logical or and a logical and. In logical “or” if at least one of the inputs is true or high then the output is true or high whereas in logical “and” only when all of the inputs are true output will be true.