Symbolize the following argument and then determine its vali

Symbolize the following argument and then determine its validity using a Shortened Truth Table:

Symbolize the following argument and then determine its validity using a Shortened Truth Table:

If either John is happy or Mary is sad, then Albert is board. But if Albert isn’t bored, then Fred is tired. Of course Fred isn’t tired, and if Albert is bored, then Wendell is annoyed. So obviously Wendell is annoyed unless John is happy.

Solution

Let \"John is happy\" be denoted by J

\"Mary is sad\" be denoted by M

\"Albert is board\" be denoted by A

\"Fred is tired\" be denoted F

\"Wendell is annoyed\" by W

If either John is happy or Mary is sad, then Albert is board. This sybolically written as

P1 : (J AND NOT M) OR (NOT J AND M) --->A

P2 : if Albert isn’t bored, then Fred is tired. written as NOT A ---> F

P3: Of course Fred isn’t tired, written as   , NOT F

P4: if Albert is bored, then Wendell is annoyed. is written as A---->W

From P3 and P2 A is TRUE. This along with P4 gives us W is TRUE.