Discrete Mathematics Answers

How is a set with one element in it called?

Use Mathematical Induction to prove the following:
(i) 1
2 + 22 + 32 + … + n
2 =

Write a sequence formula?????

1,4,9,16,25,.........

without using truth table prove that
¬(p↔q) and ¬p↔q are logically equivalent.

without using truth table prove that
[(p˅q)˄(p→r)˄(q→r)]→r is a tautology.

Without using truth table prove that (p→q)ᴧ(q→r)→(p→r) is a tautology

(A Å B) Å(C Å D) = (A Å D) Å (B Å C)

where Å is the Symmetric Difference

suppose repetation are not permited the digit is 1,2,3,4,5,7
how many such no are less than 4000?

In a survey of a TriDelt chapter with 50 members, 19 were taking mathematics, 35 were taking English, and 9 were taking both. How many were not taking either of these subjects?

Prove that if A and B are any two sets such that A is proper subset of B, then A union B=B-
1) by direct method
2) by proving its contrapositive.
3) by contradiction.