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C192006 Pages:3

(1) All apples red. (14) Some students are brilliant
Check the validity of the following argument:

“Tf एला the job and work hard, then I will get promoted. If 1 get promoted ,
then I will be happy. Therefore ,either I will not get the job or I will not work
hard.”

Differentiate between free and bound variables with suitable examples.

Derive the following using Rule CP if necessary

(a) |? ५०, 10೫೩ ೫೩5ಎ PS (0) 7-२ (QR), Q> (RS) = P (QS)
Show that (x) (P(x) ५ Q(x)) = (x)P(x) ५ (उ x)Q(x) using Indirect method of
Proof .

Show the following using indirect method of Proof

(8-0), RYS, 520,220 =P

Show by Mathematical Induction that n3 + n is divisible by 3.

An island has two tribes of natives. Any native from the first tribe always tells
the truth, while the other tribe always lie.If you arrive at the island and ask a
native if there is gold on the island. He answers “ There is gold on the island if
and only if I always tell the truth.”Is there gold on the island? Justify your
answer with the help of truth table.

Show that from (i)(Ox)(F(x)A S(x)) - (y)(M(y) - W(y)) and

(ii)(y)(M(y) | W(y)) the conclusion (x)(F(x) - | S(x)) follows.
Show that ](P ^ 0) ‏ماج‎ v ) |? VQ)) <=> ( |? VQ )( without constructing truth

table)

Show that “ If x is an integer and x’ is even, then x is also even” by proof by

contrapositive method.

KKK

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