1
GATE CSE 1999
MCQ (More than One Correct Answer)
+2
-0
Which of the following sets of component(s) is/are sufficient to implement any arbitrary Boolean function?
A
$$XOR$$ gates, $$NOT$$ gates
B
$$2$$ to $$1$$ multiplexers
C
$$AND$$ gates, $$XOR$$ gates
D
Three-input gates that output $$(A.B) + C$$ for the inputs $$A. B$$ and $$C.$$
2
GATE CSE 1999
MCQ (Single Correct Answer)
+1
-0.3
Which of the following functions implements the Karnaugh map shown below? GATE CSE 1999 Digital Logic - K Maps Question 7 English
A
$$\overline A B + CD$$
B
$$D\left( {C + A} \right)$$
C
$$AD + \overline A B$$
D
$$(C + D)(\overline C + D)(A + B)$$
3
GATE CSE 1999
MCQ (More than One Correct Answer)
+2
-0
Zero has two representations in:
A
Sign magnitude
B
$$1's$$ complement
C
$$2's$$ complement
D
None of the above
4
GATE CSE 1999
Subjective
+2
-0

(a) Mr. X claims the following:
If a relation R is both symmetric and transitive, then R is reflexive. For this, Mr. X offers the following proof.

"From xRy, using symmetry we get yRx. Now because R is transitive, xRy and yRx togethrer imply xRx. Therefore, R is reflextive."


Briefly point out the flaw in Mr. X' proof.

(b) Give an example of a relation R which is symmetric and transitive but not reflexive.