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If p = a number from {8, 9, 10, 11, 12}
q = not a composite number
r = a square number
s = a prime number
then what is the value of ~((p → ~q)∧(~r ∨~S) )
  • a)
    8, 9, 10, 11, 12
  • b)
    8, 9, 10
  • c)
    11, 12
  • d)
    11
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
If p = a number from {8, 9, 10, 11, 12}q = not a composite numberr = a...
To find the value of ~((p < q)="" ∧="" (r="" ∧="" s)),="" we="" need="" to="" evaluate="" each="" condition="" />

Given:
p = a number from {8, 9, 10, 11, 12}
q = not a composite number
r = a square number
s = a prime number

First, let's determine the value of (p < />
Since q is not a composite number, it must be a prime number. The numbers in the set {8, 9, 10, 11, 12} are not prime numbers. Therefore, p cannot be less than q. Thus, (p < q)="" is="" />

Next, let's determine the value of (r ∧ s):
r represents a square number and s represents a prime number.

The square numbers in the set {8, 9, 10, 11, 12} are: 9 (3^2) and 10 (since the square root of 10 is not an integer, 10 is not a square number).
The prime numbers in the set {8, 9, 10, 11, 12} are: 11

Therefore, (r ∧ s) is true.

Now, let's evaluate ~((p < q)="" ∧="" (r="" ∧="" />
Since (p < q)="" is="" false="" and="" (r="" ∧="" s)="" is="" true,="" we="" have="" ~((p="" />< q)="" ∧="" (r="" ∧="" s))="~(false" ∧="" />

The negation of the conjunction (false ∧ true) is equivalent to the disjunction (¬false ∨ ¬true).
¬false is true, and ¬true is false.
So, ~(false ∧ true) = true ∨ false = true.

Therefore, the value of ~((p < q)="" ∧="" (r="" ∧="" s))="" is="" true.="" q)="" ∧="" (r="" ∧="" s))="" is="" />
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Community Answer
If p = a number from {8, 9, 10, 11, 12}q = not a composite numberr = a...
Given that, If p = a number from {8, 9, 10, 11, 12}
q = not a composite number
r = a square number
s = a prime number
~((p→~ q)∧(~r ∨~S) )
¬((p→¬q)∧(¬r∨¬S))
¬(¬p∨¬q)∨¬(¬r∨¬S)
(p∧q)∨(r∧s)
p∧ q = {8, 9, 10, 11, 12} ∧  {11 } = {11}
(r ∧ s) = { a square number }∧{ a prime number}
(r ∧ s) = {9} ∧ {11} = { }
(p∧ q) ∨ (r ∧ s)= {11} ∨ { } = {11}
Hence the correct answer is 11.
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If p = a number from {8, 9, 10, 11, 12}q = not a composite numberr = a square numbers = a prime numberthen what is the value of ~((p → ~q)∧(~r ∨~S) )a)8, 9, 10, 11, 12b)8, 9, 10c)11, 12d)11Correct answer is option 'D'. Can you explain this answer?
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