Tuesday, 4 August 2015

Discrete Structure Unit-I MCQs



:  Which of the following propositions is tautology?
A.
(p v q)→q
p v (q→p)
p v (p→q)
Both (b) & (c)
2:  Which of the proposition is p^ (~ p v q) is
A tautulogy
A contradiction
Logically equivalent to p ^ q
All of above
3:  Which of the following is/are tautology?
a v b → b ^ c
a ^ b → b v c
a v b → (b → c)
None of these
4:  Logical expression ( A^ B) → ( C' ^ A) → ( A ≡ 1) is
Contradiction
Valid
Well-formed formula
None of these
5:  Identify the valid conclusion from the premises Pv Q, Q → R, P → M, ˥M
P ^ (R v R)
P ^ (P ^ R)
R ^ (P v Q)
Q ^ (P v R)
6:  Let a, b, c, d be propositions. Assume that the equivalence a ↔ (b v ˥b) and b ↔ c hold. Then truth value of the formula ( a ^ b) → ((a ^ c) v d) is always
True
False
Same as the truth value of a
Same as the truth value of b
7:  Which of the following is a declarative statement?
It's right
He says
Two may not be an even integer
I love you
8:  P → (Q → R) is equivalent to
(P ^ Q) → R
(P v Q) → R
(P v Q) → ˥R
None of these
9:  Which of the following are tautologies?
((P v Q) ^ Q) ↔ Q
((P v Q) ^ ˥P) → Q
((P v Q) ^ P) → P
Both (a) & (b)
10:  If F1, F2 and F3 are propositional formulae such that F1 ^ F2 → F3 and F1 ^ F2→F3 are both tautologies, then which of the following is TRUE?
Both F1 and F2 are tautologies
The conjuction F1 ^ F2 is not satisfiable
Neither is tautologies
None of these
11:  Consider two well-formed formulas in propositional logic
        F1 : P →˥P F2 : (P →˥P) v ( ˥P →)
       Which of the following statement is correct?
F1 is satisfiable, F2 is unsatisfiable
F1 is unsatisfiable, F2 is satisfiable
F1 is unsatisfiable, F2 is valid
F1 & F2 are both satisfiable
12:  What can we correctly say about proposition P1:
        P1 : (p v ˥q) ^ (q →r) v (r v p)
P1 is tautology
P1 is satisfiable
If p is true and q is false and r is false, the P1 is true
If p as true and q is true and r is false, then P1 is true
13:  (P v Q) ^ (P → R )^ (Q →S) is equivalent to
S ^ R
S → R
S v R
All of above
14:  The functionally complete set is
{ ˥, ^, v }
{↓, ^ }
{↑}
None of these
15:  (P v Q) ^ (P→R) ^ (Q → R) is equivalent to 
P
Q
R
True = T
16:  ˥(P → Q) is equivalent to
P ^ ˥Q
P ^ Q
˥P v Q
None of these
17:  In propositional logic , which of the following is equivalent to p → q?
~p → q
~p v q
~p v~ q
p →q
18:  Which of the following is FALSE?
Read ^ as And, v as OR, ~as NOT, →as one way implication and ↔ as two way implication?
((x → y)^ x) →y
((~x →y)^ ( ~x ^ ~y))→y
(x → ( x v y))
((x v y) ↔( ~x v ~y))
19:  Which of the following well-formed formula(s) are valid?
((P → Q)^(Q → R))→ (P → R)
(P → Q) →(˥P → ˥Q)
(P v (˥P v ˥Q)) →P
((P → R) v (Q → R)) → (P v Q}→R)
20:  The correct prefix formula is
→˥,P v Q ↔˥R ˥S
→P˥Qv ↔ ˥R
→→PQ→→QR→PR

→˥PV ↔ QSP

21. A _______ is an ordered collection of objects.

A. Relation
B.  Function
C. Set
D. Proposition

22. The Cartesian Product B x A is equal to the Cartesian product A x B. Is it True or False?

A) True
B) False

23. The members of the set S = {x | x is the square of an integer and x < 100} is _________________.

A. {0, 2, 4, 5, 9, 58, 49, 56, 99, 12}
B.  {0, 1, 4, 9, 16, 25, 36, 49, 64, 81}
C. {1, 4, 9, 16, 25, 36, 64, 81, 85, 99}
D. {0, 1, 4, 9, 16, 25, 36, 49, 64, 121}

24. In a Venn diagram , the overlap between two circles represents:

A.  the union of two sets
B.  the intersection of two sets
C.  the elements that are in either of two sets
D.  the difference between the number of elements in two sets

25. The set (A-B)-C is equal to the set

A.    (A-B)∩C
B.    (AUB)-C
C.    (A-B)UC
D.     A-(BUC)

26. In a class of 40 students, 12 enrolled for both English and German. 22 enrolled for German. If the students of the class enrolled for at least one of the two subjects, then how many students enrolled for only English and not German?

A. 30

B. 10
C. 18
D. 28
E. 32







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