Math for Computer science Questions and Answers 261 to 270

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.
262.
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.
263.
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.
264.
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.
265.
Which of the following functions is not one-one defined over the set of positive integers?
(a)  x2                     (b)  x–1                   (c)  x+1                   (d)  2x+1                 (e)  4x.
266.
Let p(x) be the statement “x = x2”. 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.
267.
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.
268.
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.
269.
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).
270.
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 (pq) p. So the rule of inference used is modus ponens.
262.
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 pq is ¬q¬p. Hence the answer.
263.
Answer : (b)
Reason : A is called a proper subset of B if AB and A  B then
264.
Answer : (b)
Reason : P(c) for an arbitrary c,  xP(x) is universal generalization.
265.
Answer : (a)
Reason : The function x2 is not one-one over a set of +ve integers because more than one value of the domain are mapped to a single value of the co-domain. For eg. f(2) = f(–2) = 4.
266.
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.
267.
Answer : (c)
Reason : From the definition of  fallacy of begging the question.
268.
Answer : (e)
Reason : From the definition of set difference.
269.
Answer : (a)
Reason : Duplicated elements are considered to be same in sets.
270.
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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