For the statement S1 and S2 below, component statement indicated. Do the following

i) Write the given statement using quantifiers, and express your answer using a conjunction.

ii) Write its negation using quantifiers, and express your answer using a conjunction.

iii)Decide( T/F) whether the staements t1 and t2 are the negations of S1 and S2 respectively.

a) S1 denotes the statements:" Some rich men make it into the kingdom of heaven."

Let r(x) be the statement:" x is a rich men" and k(x) " x makes it into the kingdom of heaven"

i) S1______________________________________________________________________

ii) ~S1_____________________________________________________________________

iii) t1" some rich men don't make it into the kingdom of heaven" (T/F)

b) S2 denotes the statement: " All even integer are divisible by 2"

Let e(x) be the statement: " x is an even integer" and d(x): " x is divisible by 2"

i) S2__________________________________________________________

ii) ~ S2________________________________________________________

iii) t2 " No even integers are divisible by 2" ( T/F)_______________