Find the product:
`(p - 1/p) ( p + 1 /p ) ( p ^ 2 + 1/ p ^2) ( p^4 + 1/ p ^ 4 )`

Find the products: (7p^4+q)(49 p^8-7p^4q+q^2)

If p + 1/( p + 2 ) = 3 , find the value of ( p + 2 )^3 + 1/( p + 2 )^3

If 1 (I) p^2 (II) p^2 = 2p (III) p^2 > 2p

Find the value of : 1/2 p^(2) xx 4p^(2)q xx(-3 p)

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 )

Sum the following infinite series (p-q) (p+q) + (1)/(2!) (p-q)(p+q) (p^(2) + q^(2))+(1)/(3!) (p-q) (p+q) (p^(4)+q^(4)+p^(2) q^(2)) + ...oo

If E and F are events such that P(E) = 1/4, P(F) =1/2 and P(E and F) = 1/8, find (i) P(E or F) , (ii) P( - E and - F).

The least value of the quadratic polynomial, f(x) = (2p^(2) + 1) x^(2) + 2 (4p^(2) - 1) x + 4(2p^(2)+1) for real values of p and x is

If A and B are events such that P(A) = 1/2 , P(B) = 1/3 and P(A cap B) = 1/4 then find P(A |B)

If A and B are two events such that P(A) = (1)/(4), P(B) = (1)/(2) and P(A cap B) = (1)/(8) , find P (not A and not B).