Math for Computer science
Questions 261 to 270
261.

“If it is rainy,
then the pool will be closed. It is rainy. Therefore, the pool is closed.”
The rule of inference used is _________.
(a) Addition (b) Simplification
(c) Modus ponens
(d) Modus
tollens (e) Hypothetical syllogism.

The contrapositive
of the implication given below
“I come to the class whenever there is
going to be a quiz.”
(a) If there is going to be a quiz, I come to class
(b) If I
come to class, there will be a quiz
(c) If I
do not come to class, then there will not be a quiz
(d) If
there is not going to be a quiz, then I will not come to the class
(e) If
there is not going to be a quiz, then I will come to the class.


A is a subset of B
but A _{} B then A is called ______ of B.
(a) superset (b) proper subset (c) power set (d)
null set (e)
sample set.


The name given to
the rule of inference P(c) for an
arbitrary c, _{}xP(x)
is
(a) Universal
instantiation (b) Universal generalization
(c)
existential instantiation (d) existential generalization
(e)
Universal quantification.


Which of the
following functions is not oneone defined over the set of positive integers?
(a) x^{2} (b) x–1 (c) x+1 (d) 2x+1 (e) 4x.


Let p(x) be the
statement “x = x^{2}”. If the universe of discourse consists of the
integers which one of the following propositions is false?
(a) P(0) (b) P(1) (c) _{}xp(x)
(d)
For all p(x) (e) Both (a) and (b) are false.


The fallacy
occurring when one or more steps of the proof are based on the truth of the
statement being proved
(a) Fallacy of denying the hypothesis
(b) Fallacy
of affirming the conclusion
(c) Fallacy
of begging the question
(d) Fallacy
of denying the conclusion
(e) Fallacy
of affirming the hypothesis.


The set containing
those elements that are in A but not in B where A and B are two sets is
denoted by
(a) A _{} B (b) A _{} B (c) A _{} B (d) A _{} B (e) A – B.


Which of the
following pairs of sets are equal?
(a) {1,3,3,3,5,5,5,5,5}, {1,3,5} (b) {{1}}, {1,{1}} (c) _{}, {_{} }
(d) (a) and (b) (e) (b) and (c).


The range of the
function that assigns to a bit string the number of times the block 11
appears in the bit string.
(a)
set of integers (b) set of whole numbers (c) set of real numbers
(d)
set of all bit strings (e) set of
irrational numbers.

Answers
261.

Answer : (c)
Reason : The compound propositions given are in s the
form (p_{}q) _{}p. So the rule of inference used is
modus ponens.

Answer : (c)
Reason : The given statement in if – then form is “If
there is going to be a quiz then I come to the class.” The contrapositive of
an implication p_{}q is ¬q_{}¬p. Hence the answer.


Answer : (b)
Reason : A is called a proper subset of B if A_{}B and A _{} B then


Answer : (b)
Reason : P(c)
for an arbitrary c, _{} xP(x) is
universal generalization.


Answer : (a)
Reason : The function x^{2 }is not oneone
over a set of +ve integers because more than one value of the domain are
mapped to a single value of the codomain. For eg. f(2) = f(–2) = 4.


Answer : (d)
Reason : For all p(x) is false because if x = 2 , 2 is
not equal to 4. so For all p(x) is false.


Answer : (c)
Reason : From the definition of fallacy of begging the question.


Answer : (e)
Reason : From the definition of set difference.


Answer : (a)
Reason : Duplicated elements are considered to be same
in sets.


Answer : (b)
Reason : The function assigns the number of times the
block 11 appears in the bit string. It can be from 0 to any number. So the
answer is the set of whole numbers.

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