Mathematical Statements and truth Values

Question

P - the sun is shining
q - it is raining
r - the cat is inside


a - the sun is shining and the cat is inside.
b - if it is raining then the sun is not shining
c - if it is not raining the cat is not inside

 

i have been trying to figure this out all day and my brain has hit a wall.

any help would be greatly appreciated

Thank you! 

Answer 1

Are you trying to write out a,b,c?

 

well a is and AND statement.

a = P^r

 

b is a if then statement. However note the sun is not shining so we are taking not P.

b = Q->~(P) (~P is not P).

 

c is a if then statement as well with not statements. 

c = ~(Q)->~(r)

Note this is equivalent to r -> Q

(if the cat is inside then it is raining)

Hipe helpful 

best - david