Subtract `3p q\ (p-q) `from` 2p q\ (p+q)`

Subtract 3pq(p-q) from 2pq(p+q)

Subtract : 5p - 3q - 2r " from " 7p + 2q - 5r

Subtract p - 2q + r " from the sum of " 10 p - r and 5p + 2q

Which of the following statement is not a fallacy? Option1 p ∧ ( ~ ( ~ p ⇒ q ) ) Option2 ~ ( ( p ∧ q ) ⇒ p ) Option3 ~ ( p ⇒ ( p ∨ q ) ) Option4 ~ p ∨ ( ~ p ⇒ q )

(a) If r^(2) = pq , show that p : q is the duplicate ratio of (p + r) : (q + r) . (b) If (p - x) : (q - x) be the duplicate ratio of p : q then show that : (1)/(p) + (1)/(q) = (1)/(r) .

If p= q + 2 then p gt q .

The incorrect statement is (A) p →q is logically equivalent to ~p ∨ q. (B) If the truth-values of p, q r are T, F, T respectively, then the truth value of (p ∨ q) ∧ (q ∨ r) is T. (C) ~(p ∨ q ∨ r) = ~p ∧ ~q ∧ ~r (D) The truth-value of p ~ (p ∧ q) is always T

if p: q :: r , prove that p : r = p^(2): q^(2) .

Observe the following statements I : The dual of [ ~p ^^ q)] vv [ p ^^ {~(q vv ~s)}] is [~(p vv q)] ^^ [p vv{~(q ^^ ~s)}] II : The dual of ~p ^^ [(~q) ^^ (p vv q) ^^ ~r] is ~p vv[~q) vv(p ^^ q) vv ~r] The true statements in the above is/are :

Given that q^2-p r ,0,\ p >0, then the value of |p q p x+q y q r q x+r y p x+q y q x+r y0| is- a. zero b. positive c. negative \ d. q^2+p r