FOCS
Assignment – I
Q 1. Let p be ``Erik reads Newsweek '', let q be ``Erik reads The New Yorker '', and let
r be ``Erik reads Time ''. Write each of the following in symbolic form:
a) Erik reads Newsweek or The New Yorker , but not Time.
b) Erik reads Newsweek and The New Yorker , or he does not read Newsweek
and Time.
c) It is not true that Erik reads Newsweek but not Time.
d) It is not true that Erik reads Time or The New Yorker but not Newsweek.
Q2. Use the laws to show that :
~ (p v q) V ( ~p Λ
q) Ξ
~p
Q3. Draw the truth table of [ p ―› (( q Λ ( ~t)) V s ] Λ [(~t) ‹―› (s Λ q )] . Also find he truth
value of the same where t is false and p,q,s are true.
Q4. Prove the the following arugment is valid : p ―› ~ q , r ―› q , r |― ~p
Q5. Test the validity of the argument:
If I study , then I will not fail mathematics .
If I do not play basketball, then I will Study.
But I failed mathematics.
______________________________________________________
Therefore, I must have played basketball.
Q6. Consider the statement and write its converse, inverse and contrapositive : If flood
destroys my house or fire detroy my house then my insurance company will pay me.
Q7. Give an indirect proof of theorem “ if 3n+2 is odd , then n is odd.”
Q8. Obtain the CNF of ~(p v q) ‹―› (p Λ q)
Q9. Let A= { 1,2,3,4,5 }. Determine the truth values of each of the following statements.
(A) ( ∃ x є A) ( x+3 = 10)
(b) ( ∀ x є A) ( x+3 < 10)
(c) ( ∃ x є A) ( x+3 < 5 )
(d) ( ∀ x є A) ( x+3 ≤ 7)
Also negate each of the statements.
Q10. Find the dnf of (~p ―› r) Λ (p ‹―›q).