How many words can be formed using letter of PEPSUDENT using each letter at most once?

i) If each letter must be used,

ii) If some or all the letters may be omitted

What is a relation? Explain equivalence relation with the help of an example.

Prove that 2ⁿ > n³, ∀n ≥ 10

Make truth table for followings.

 i) p→(~ ˅  ˅q) ˅ (~p ˅ r)

 ii) p→ (~r  ˅~ q) (p  ˅~ r)

Explain principal of duality with the helpof example.

Three Sets A, B and C are: A = {1, 2, 8,9,12,15,17}, B = { 1,2, 3 ,4, 10 } and C {7, 9, 10, 11, 13}. Find A U B A C ; A A ~B A U U C; A A B U C and (A A ~C).

Write the following statements in symbolic form: 

(a) Shyam is rich but unhappy

(b) Either do physical exercise or be ready for poor health