Is this argument valid Clearly indicate if it is valid or in

Is this argument valid? Clearly indicate if it is valid or invalid, and show your work. p q p ~q Is this argument valid? a (b c) ~ (b c) a Is this argument valid? Show your work. p q q r r

Solution

1)

No it is not valid. Consider p=T and q=F

Then pvq=TvF=T

p=T

q=F

Hence, the premises are true but lead to a false conclusion

2) a v (b * c)

~ (b*c)

a

Is true. a v (b*c) means at least one of a and b*c is true

the second premise says b*c is not true.

Hence a must be true.

3) p->q

q->r

r

This is false. Consider r=F, q=F, p=F

Then p->q is F->F which is true

q->r is F->F which is also true

But r=F which. Hence, true premises lead to false conclusion. This means the argument is invalid.