Question

This is a subjective question, hence you have to write your answer in the Text-Field given below.
(a) Show that P→ Q and (PAQ) V (p^-Q) are equivalent.
(b) Express each of these following statement into logical expression using predicates, quantifiers, and logical co a. No student is perfect b. Not everyone is perfect.
c. All your relatives are perfect
d. At least one of your relative is perfect.
e. Everyone is your relative and is perfect.​

Answer 1

Answer:

a) Namely, p and q are logically equivalent if p ↔ q is a tautology. If p and q are logically equivalent, we write p ≡ q. Example: ... So (p → q) ↔ (q ∨ ¬p) is a tautology.

a) No one is perfect. == Not ( one is perfect) = ~ (∃x(px))= ∀x ~p(x)= Every one is imperfect.

b) Not everyone is perfect.== Not (everyone is perfect.)= ~( ∀x(px))=∃x ~p(x)= Atleast one is imperfect.

c) All your friends are perfect. == if there is a person who is your friend then he is perfect== ∀x( F(x)→P(x))

d) At least one of your friends is perfect. == There is a person who is your friend who is perfect.

∃x (F(x)∧P(x))

Step-by-step explanation:

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