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# Discrete Mathematics – Q&A

174Questions:

without using truth table prove that
[(p˅q)˄(p→r)˄(q→r)]→r is a tautology.
without using truth table prove that
¬(p↔q) and ¬p↔q are logically equivalent.
Write a sequence formula?????

1,4,9,16,25,.........
Use Mathematical Induction to prove the following:
(i) 1
2 + 22 + 32 + … + n
2 =
Q. where the concept of a function first arose? Also find that who has arosed this concept? Also describe How this concept was first used?
who has developed the concept of congurences and when he developed the concept?
Who has developed the concept of congurences and when has he developed the concept?
A relation R defined on a set S is said to be ………… if b R a
∀a,b∈S
.
a. transitive
b. reflexive
c. symmetric
d. none of the above
For each of the following words: if it is a sentence in the grammar, draw its derivation
tree; if it is not a sentence, explain carefully how you know that it is not a sentence.

(i) a/b − c/d ∗ e + f