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Discrete Mathematics – Q&A

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In the context of admission to IGNOU, give example of the following-
1.an implication ,
2.the converse of (1) above.
3.a two way implication which is true.
4.a statement involving both for all and there exit.
5.the contrapositive of (1) above.
Answered!
Any subset of A × A is called a relation on the set A. A relation R on A is symmetric if
(a, b) ∈ R ⇒ (b, a) ∈ R ∀ a, b ∈ A. Give one example each, with justification, of
i) a symmetric relation on ,
ii) a relation that is not symmetric on the set {2, 3, 5, 7}.
Answered!
In a survey of a TriDelt chapter with 50 members, 19 were taking mathematics, 33 were taking English, and 7 were taking both. How many were not taking either of these subjects?
Answered!
In the context of admission to IGNOU, give examples of the following:
i) an implication;
ii) the converse of (i) above;
iii) a two-way implication which is true;
iv) a statement involving both ∀ and ∃.
v) the contrapositive of (i) above.
Answered!
Any subset of A × A is called a relation on the set A. A relation R on A is symmetric if
(a, b) ∈ R ⇒ (b, a) ∈ R ∀ a, b ∈ A. Give one example each, with justification, of
i) a symmetric relation on ,
ii) a relation that is not symmetric on the set {2, 3, 5, 7}.
Answered!
write the following boolean expressions in an equivalent sum of product canonical form in three variables x1, x2, and x3:
1. x1*x2 ?
2. x1⊕x2 ?
3. (x1⊗X2)'*X3
Answered!
Simplify the following Boolean function using k -map
F = A’C + A’B + AB’C + BC
Answered!
Expand the following Boolean functions into their canonical form:
i. f(X,Y,Z)=XY+YZ+X'Z+X'Y'
ii. f(X,Y,Z)=XY+X'Y'+X'YZ
Answered!
Expand the following Boolean functions into their canonical form:
i. f(X,Y,Z)=XY+YZ+ X Z+ X Y
ii. f(X,Y,Z)=XY+ X Y + X YZ
Answered!
If we have 100 people (80 male and 20 female) and we need to choose a committee.
The committee must contain exactly 2 females, then how many different 5 person committees are possible?
Answered!
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