Find the truth value
Neither $21$ is a prime number nor it is divisible by $3$

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Solution

From the statement given,
$21$ is divisible by $3$
$∵$ $21 = 3 \times 7$
$\Rightarrow$ $21$ is also not prime
So, $\neg (21 ϵ P) Λ \neg (3 / 21)$
$= \neg f a l s e Λ \neg T$
$= T Λ F$
$= F$
$∴$ the truth value of the statement is false.

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(ii) If a number is divisible by 9, it must be divisible by 3.
(iii) If a number is divisible by 4, it must be divisible by 8.
(iv) If a number is divisible by 8, it must be divisible by 4.
(v) A number is divisible by 18, if it is divisible by both 3 and 6.
(vi) If a number is bivisible by both 9 and 10, ut nyst be divisible by 90.
(vii) If a number exactly divides the sum of two numbers, it must exactly divide the numbers separately.
(viii) If a number divides three numbers exactly, it must divede their sum exactly.
(ix) If two numbers are co-prime , at least one of them must be a prime number.
(x) The sum of two consecutive odd numbers is always divisible by 4.

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Find the truth valueNeither 21 is a prime number nor it is divisible by 3

From the statement given,21 is divisible by 3∵ 21=3×7⇒ 21 is also not primeSo, ¬(21ϵP)Λ¬(3/21)=¬falseΛ¬T=TΛF=F∴ the truth value of the statement is false.

Find the truth value
Neither $21$ is a prime number nor it is divisible by $3$

From the statement given,
$21$ is divisible by $3$
$∵$ $21 = 3 \times 7$
$\Rightarrow$ $21$ is also not prime
So, $\neg (21 ϵ P) Λ \neg (3 / 21)$
$= \neg f a l s e Λ \neg T$
$= T Λ F$
$= F$
$∴$ the truth value of the statement is false.