Each of the following expressions is intended to be a single, compound symbolic

Question

Each of the following expressions is intended to be a single, compound symbolic sentence in SL, but some of them are incorrectly written. Figure out which of these is a well-formed sentence. If it is well-formed, translate it into relatively idiomatic English using the Translation Scheme below. If it is not well-formed say “not a wff”. You should not attempt to translate any non-wffs. Translation Scheme: A := “Apples are red.” K := “Kangaroos are jumpy.” B := “Bananas are yellow.” M := “Monkeys are funny.” C := “Carrots are crunchy.” P := “Parrots are noisy.”

1. A & ~M

~A ~C

K( & ~M)

A, B

~ P & M

~A & B

A BC

K (~M)

A & B C

(~A) & B

A, B, & C

~(A & B)

(~A)( & B)

(K M) ~P

K (M ~P)

M & (~P & ~M) P

(M & ~P) & (~M P)

~(~A) & ((~B) & (~C))

~(~(~M)) & ~~~P

~(B ~C) (~B & C)

Explanation / Answer

A & ~M - Apples are red and Monkeys are not funny.

~A ~C - if Apples are not red then Carrots are not crunchy

K( & ~M) - Kangaroos are jumpy and Monkeys are not funny

A, B -not a wff

~ P & M - Parrots are not noisy and  Monkeys are funny

~A & B -Apples are not red and Bananas are yellow

A BC -if Apples are red then Bananas are yellow and Carrots are crunchy

K (~M) - Kangaroos are jumpy or  Monkeys are not funny.

A & B C -Apples are red and  Bananas are yellow or Carrots are crunchy.

(~A) & B -Apples are not red and Bananas are yellow

A, B, & C - not a wff

~(A & B) - Apples are not red or Bananas are not yellow

(~A)( & B) -Apples are not red or Bananas are yellow

(K M) ~P - Kangaroos are jumpy or Monkeys are funny or Parrots are not noisy

M & (~P & ~M) P -Monkeys are funny and (Parrots are noisy or Monkeys are not funny ) and ( Parrots are noisy or Parrots are not noisy)

(M & ~P) & (~M P)= ~P M    - Parrots are not noisy or Monkeys are funny

~(~A) & ((~B) & (~C)) - Apples are red and Bananas are not yellow and   Carrots are not crunchy

~(~(~M)) & ~~~P - Monkeys are not funny and Parrots are not noisy

~(B ~C) (~B & C) - if Bananas are yellow or Carrots are not crunchy is false then Bananas are not yellow and Carrots are crunchy

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