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Discrete Mathematics – Q&A

173Questions:

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

1,4,9,16,25,.........
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Use Mathematical Induction to prove the following:
(i) 1
2 + 22 + 32 + … + n
2 =
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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?
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who has developed the concept of congurences and when he developed the concept?
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Who has developed the concept of congurences and when has he developed the concept?
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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
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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
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