(a) indicate which of the following statements are true and which are false Justify your answer.
i. Vc E Z+,3y E Z+ such that x = y+1
ii. 3c e Z+,Vy e Z+ such that c =y+1
iii. 3x E Z+,3y E Z+ such that x= y+1
(b) Given the following argument:
" The football game will be cancelled only If it rains "
'it rained, therefore the football game was cancelled"
Assume p means " it rains" whereas q means "football game cancelled'
i. Translate this argument to a symbolic form.
ii. Construct the truth table.
iii. Determine if this argument is a valid argument or not.
(c) Say whether or not the following argument is a valid argument. Explain your answer.
(a) Successful candidates for this job must have either a Master's degree or five years of work experience (b) Johnny has a Master's degree (c)Johnny got the job
(d) .:. Johnny does not have five years of work experience
d) Let P() and Q() be two predicates and suppose D is the the domain of x. For the statement forms in each pair, determine whether they have the same truth value for every choice of p(), Q() and D, or not.
i.3x E D,(P()^Q(x)),and(Sx e D,P(x))^(3x e D,Q(r)) ii.Vx e D,(P()v Q(x)),and(Vx e D,P(x))V(Vx e D,Q(c))