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Discrete Mathematics
Transform by making change of variable j = i-4.
Discrete Mathematics
Suppose S is a set containing 5 elements, and that ⪯ is a total ordering of S. Draw the Hasse diagram for ⪯ (no need to label the vertices in your diagram).
Discrete Mathematics
Definition of Function, Domain, Codomain and Range, Well defined function, Types of functions(Injective ,Surjective, Bijective, Composite)
Discrete Mathematics
) We have the following set of information about a computer program, find the mistake in the program using Rules of Inferences.
i. Either a variable is not declared or there is a syntax error in the fifth line.
ii. If there is a syntax error in the fifth line, then there is a missing semicolon or there is a mistake in variable name.
iii. There is not a missing semicolon.
iiii. There is a mistake in variable name.
i. Either a variable is not declared or there is a syntax error in the fifth line.
ii. If there is a syntax error in the fifth line, then there is a missing semicolon or there is a mistake in variable name.
iii. There is not a missing semicolon.
iiii. There is a mistake in variable name.
Discrete Mathematics
) We have the following set of information about a computer program, find the mistake in the program using Rules of Inferences.
i. Either a variable is not declared or there is a syntax error in the fifth line.
ii. If there is a syntax error in the fifth line, then there is a missing semicolon or there is a mistake in variable name.
iii. There is not a missing semicolon.
iiii. There is a mistake in variable name.
i. Either a variable is not declared or there is a syntax error in the fifth line.
ii. If there is a syntax error in the fifth line, then there is a missing semicolon or there is a mistake in variable name.
iii. There is not a missing semicolon.
iiii. There is a mistake in variable name.
Discrete Mathematics
Use mathimatical Induction to prove that
1²+2²+3²+.......n²= n(n+1)(2n+1) divided by 6
1²+2²+3²+.......n²= n(n+1)(2n+1) divided by 6
Discrete Mathematics
Solve the following recurrence relations
i) Fn= Fn-1 +Fn-2 where a1=a2=1
ii) an=2an-1 - an-2 +2 where a1 = 1 and a2 = 5
i) Fn= Fn-1 +Fn-2 where a1=a2=1
ii) an=2an-1 - an-2 +2 where a1 = 1 and a2 = 5
Discrete Mathematics
1.Determine whether ¬(p∨(¬p∧q)) and ¬p∧¬q are equivalent without using truth table.
2.Determine whether the compound proposition ~(p∨q)∨(~p∧q)∨p to tautology.
3.Determine whether (p → q)∧(p → r)≡p → (q ∧r) using a truth table
2.Determine whether the compound proposition ~(p∨q)∨(~p∧q)∨p to tautology.
3.Determine whether (p → q)∧(p → r)≡p → (q ∧r) using a truth table
Discrete Mathematics
a) We have the following set of information about a computer program, find the mistake in the program using Rules of Inferences.
i. Either a variable is not declared or there is a syntax error in the fifth line.
ii. If there is a syntax error in the fifth line, then there is a missing semicolon or there is a mistake in variable name.
iii. There is not a missing semicolon.
iv. There is a mistake in variable name.
i. Either a variable is not declared or there is a syntax error in the fifth line.
ii. If there is a syntax error in the fifth line, then there is a missing semicolon or there is a mistake in variable name.
iii. There is not a missing semicolon.
iv. There is a mistake in variable name.
Discrete Mathematics
Suppose that the domain of the propositional function P(x) consists of the integers 1, 2, 3, 4, and 5. Express these statements without using quantifiers, instead using only negations, disjunctions, and conjunctions.
a) ∃xP(x)
b) ∀xP(x)
c) ¬∃xP(x)
d) ¬∀xP(x)
e) ∀x((x=3) → P(x))∨∃x¬P(x)
a) ∃xP(x)
b) ∀xP(x)
c) ¬∃xP(x)
d) ¬∀xP(x)
e) ∀x((x=3) → P(x))∨∃x¬P(x)
