June 2015 - Paper 2

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6:  

Consider the following statements :

(a) Boolean expressions and logic networks correspond to labelled acyclic digraphs.

(b) Optimal boolean expressions may not correspond to simplest networks.

(c) Choosing essential blocks first in a Karnaugh map and then greedily choosing the largest remaining blocks to cover may not give an optirnal expression-

Which of these statement(s) is/ are correct

A.	(a) only
B.	(b) only
C.	(a) and (b)
D.	(a), (b) and (c)
	Answer Report Discuss
	Option: D Explanation : Click on Discuss to view users comments. Write your comments here: Updating your Comments.. Updating your Comments..

7:  

Consider a full adder with the following input values :

(a) x=1, y=0 and C_i(carry input) = 0

(b) x=0, y=1 and C_i = 1

Compute the values of S(sum) and C₀ (carry output) for the above input values.

A.	S=1 , C0= 0 and S=0 , C0= 1
B.	S=0 , C0= 0 and S=1 , C0​= 1
C.	S=1 , C0= 1 and S=0 , C0​= 0
D.	S=0 , C0= 1 and S=1 , C0​= 0
	Answer Report Discuss
	Option: A Explanation : 1 0 0=01->carry 0,sum=1;0 1 1=10->carry 1,sum=0; Click on Discuss to view users comments. D.Krishnakumar said: (8:15pm on Monday 29th June 2015) (A) is correctExplanation1 0 0=01->carry 0,sum=1;0 1 1=10->carry 1,sum=0; Write your comments here: Updating your Comments.. Updating your Comments..

8:  

"lf my computations are correct and I pay the electric bill, then I will run out of money. If I don't pay the electric biIl the power will be turned off. Therefore, if I don't run out of money and the power is still on then my computations are incorrect."

Convert this argument into logical notations using the variables c, b, r, p for propositions of computations, electric bills, out of money and the power respectively. (Where  ¬ means NOT)

A.	if (c ∧ b) → r and ¬b → ¬p, then (¬r∧p)→¬c
B.	if (c ∨ b) → r and ¬b → ¬p, then (r∧p)→c
C.	if (c ∧ b) → r and ¬p → ¬b, then (¬r ∨ p)→¬c
D.	if (c ∨ b) → r and ¬b → ¬p, then (¬r∧p)→ ¬c
	Answer Report Discuss
	Option: A Explanation : Click on Discuss to view users comments. Jayanthi Ganapathi said: (5:27am on Tuesday 28th July 2015) option D is correct Jayanthi Ganapathy said: (5:28am on Tuesday 28th July 2015) Option A is correct not option D Write your comments here: Updating your Comments.. Updating your Comments.. ¬ means NOT) '>

9:  

Match the following:

List - I	List - II
(a) (p →q) ⇔ (¬q → ¬p)	(i) Contrapositive
(b) [(p ∧q) →r ]⇔ [p→ (q →r)]	(ii) Exportation law
(c) (p →q)⇔ [(p ∧ ¬q) →o]	(iii) Reductio ad absurdum
(d) (p⇔q)⇔ [(p →q) ∧(q→p)]	(iv) Equivalence

 

A.	(a)  (b)  (c)   (d) (i)   (ii)   (iii)  (iv)
B.	(a)   (b)  (c)   (d) (ii)   (iii)   (i)  (iv)
C.	(a)   (b)  (c)   (d) (iii)   (ii)   (iv)  (i)
D.	(a)   (b)  (c)   (d) (iv)   (ii)   (iii)  (i)
	Answer Report Discuss
	Option: D Explanation : Click on Discuss to view users comments. Jayanthi Ganapathy said: (5:34am on Tuesday 28th July 2015) (A) is contrapositive(B) is Exportation Law(C) is Reductio ad adburdum(D) is Equivalence Write your comments here: Updating your Comments.. Updating your Comments..

10:  

Consider a proposition given as :

" x ≥ 6, if  x2 ≥ 25 and its proof as:

If x ≥ 6, then x2 = x· x= 6· 6=36 ≥25

Which of the following is correct w.r.to the given proposition and its proof ?

(a) The proof shows the converse of what is to be proved.

(b) The proof starts by assuming what is to be shown.

(c) The proof is correct and there is nothing wrong.

A.	(a) only
B.	(c) only
C.	(a) and (b)
D.	(b) only
	Answer Report Discuss
	Option: C Explanation : Click on Discuss to view users comments. Jayanthi Ganapathy said: (5:39am on Tuesday 28th July 2015) The proof shown is converse and it assumes x>=6 to prove the statement. Write your comments here: Updating your Comments.. Updating your Comments..

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