Complete the following problems:a) Translate the following statement into mathematical English. ∀ x [ ( P ( x ) ∧ ⌝ ( x = 2 ) ) → O ( x ) ], where P(x) means "r is a prime number" and O(x) means "x is odd"b) Negate this statemem and express the result as a positive satemem (without using "no" or "nor"): There issomeone in the freshman class who doesn't have a roommate

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Complete the following problems:a) Translate the following statement into mathematical English.   ∀  x  [  (  P  (  x  )  ∧  ⌝  (  x  =  2  )  )  →  O  (  x  )  ], where P(x) means &quot;r is a prime number&quot; and O(x) means &quot;x is odd&quot;b) Negate this statemem and express the result as a positive satemem (without using &quot;no&quot; or &quot;nor&quot;): There issomeone in the freshman class who doesn&#039;t have a roommate

iljovskint · Accepted Answer

Step 1For part (a)   ∀  x (If xis a prime number and x is not equal to 2 then x is an odd number)Every prime number except 2 is an odd number.Step 2For part (b)  F  (  x  )  =  x is in the freshman class  R  (  x  ,  y  )  = x has roommate yOriginal Statement is   ∃  x  F  (  x  )  ⌝  ∃  y  R  (  x  ,  y  )Negation will be as follows:  −  ∃  x  F  (  x  )  ∧  ∃  y  R  (  x  ,  y  )  ∀  x  ⌝  (  F  (  x  )  ∧  ∃  y  R  (  x  ,  y  )  ∀  x  ⌝  F  (  x  )  ∨  ∃  y  R  (  x  ,  y  )  ∀  x  ⌝  F  (  x  )  ∨  ∃  y  R  (  x  ,  y  )  ∀  x  F  (  x  )  →  ∃  y  R  (  x  ,  y  )Everyone in the freshman class has atleast one roommate

Translate the following statement into mathematical English.

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