# Math for Computer science Questions and Answers 91 to 100

Questions and Answers Math for Computer science 91 to 100

91.
Let p, q be two inputs. If p is true and q is false then the output is false is given by
 (a) Disjunction (b) Conjunction (c) Implication (d) Boolean Sum (e) XoR operator.
92.
The fallacy of denying the hypothesis is given by
 (a) [(p ® q) Ù (Ø p)] ® (Ø q) (b) [(p ®q) Ù p] ® (Øq) (c) [(p ® q) Ù (Øp) ® q (d) [(q ® p) Ù {Øp)] ® {Øq) (e) [(q ® p) Ù (p)] ® q.
93.
A Rule of inference of the form   is called
 (a) Hypothetical Syllogism (b) Existential Instantiation (c) Universal Instantiation (d) Universal Generalization (e) Existential Generalization.
94.
If  two events can not occur simultaneously then the events are called
 (a) Independent events (b) Mutually Exclusive events (c) Dependent events (d) Impossible event (e) Certain event.
95.
A coin has been tossed for 5 times then the total number of elements in the sample space are
 (a) 2 (b) 8 (c) 16 (d) 32 (e) 64
96.
A man X hit the target for 3 times out of 8 attempts, another man Y hit the target for 5 times out of 8 attempts. What is the probability that both will hit the target?
 (a) 15/64 (b) 8/64 (c) 7/64 (d) 10/64 (e) 12/64.
97.
Inductive Hypothesis means
 (a) p(k) is true for ‘1’ (b) p(k) is true for a fixed positive integer k + 1 (c) p(k) is true for a fixed positive integer k (d) p(k) is true for a fixed positive integer k – 1 (e) p(k) is true for all n.
98.
Second principle of mathematical induction is also known as
 (a) Weak induction (b) Strong induction (c) Medium induction (d) Induction (e) Basic step.
99.
Binary equivalent of (1023)10 is
 (a) (1111111110)2 (b) (1111111011) 2 (c) (1111111111) 2 (d) (1111111101) 2 (e) (1111110111) 2.
100.
Decimal Equivalent of (10    1011       0101) 2 is
 (a) (693) 10 (b) (691) 10 (c) (695) 10 (d) (697) 10 (e) (699) 10.

91.
Reason:  By definition of implication
92.
Reason:  By definition of denying the hypothesis
93.
Reason:  By definition of exsistential generalization
94.
Reason:  By definition of mutually exclusive events
95.
Reason:  Each coin has 2 possible outcomes, it has been tossed for 5 times. So total these are                 25 = 32 possible outcomes.
96.
Reason:  A : X hits the target
B : Y hits the target
P (A) = ;  P (B) =
P (both will hit the target) = P (A) . P (B) =  .
97.
Reason:  By the definition of inductive Hypothesis
98.
Reason:  By definition of strong induction
99.
Reason:

100.
Reason:
 1 0 1 0 1 1 0 1 0 1 9 8 7 6 5 4 3 2 1 0
= 1.20 + 1.22 + 1.24 + 1.25 + 1.27 + 1.29
= 1 + 4 + 16 + 32 + 128 + 512
=(693)10