Write the component statement of the following compound statements and check whether the compound statement is true or false.
(i) 57 is divisible by 2 or 3 .
(ii) 24 is a multiple of 4 and 6.
(ii) All living things have two eyes and two legs.
(iv) 2 is an even number and a prime number.

Answer

N/a

Explanation

(i) Given compound statement is of the form 'pvq'.Since, the statement 'pvq' has the truth Value T whenever either p or q or both have the truth value T.
So ,it is true
Its component statement are
p : 57 is divisible by 2.`" "["False"]`
q: 57 is divisible by 3. `" "["true"]`
(ii) given compound statament is of the form `p^^q`. Since, the statement `p^^q` have the truth value of the truth value T whenever both p and q have the truth value T.
So, it is a ture statement .
Its component statements are
p : 24 is multiple of 4. `" "["ture"]`
q: 24 is multiple of 6.`" "["true"]`
(iii) It is a false statement. Since `q^^P` has truth value F wherever either p or q or both have the truth value F.
Its component statements are
p: All living things have two eyes.`" "["false"]`
q: All things have two eyes.`" "["false"]`
(iv) It is a true statement .
Its component statements are
p: 2 is an even number. `" "["ture"]`
q: 2 is a prime number `." "["ture"]`