UGC NET COMPUTER DECEMBER (PAPER II) 2018

In mathematical logic, which of the following are statements?
i. There will be snow in January.
ii. What is the time now?
iii. Today is Sunday.
iv. You must study Discrete Mathematics.
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Match List I with List II and choose the correct answer from the code given below.

A box contains six red balls and four green balls. Four balls are selected at random from the box. What is the probability that two of the selected balls will be red and two will be green?

A survey has been conducted on methods of commuter travel. Each respondent was asked to check Bus, Train or Automobile as a major method of travelling to work. More than one answer was permitted. The results reported were as follows:
Bus 30 people; Train 35 people; Automobile 100 people; Bus and Train 15 people; Bus and Automobile 15 people, Train and Automobile 20 people; and all the three methods 5 people. How many people completed the survey form?

Which of the following statements are true?
i. Every logic network is equivalent to one using just NAND gates or just NOR gates.
ii. Boolen expressions and logic networks correspond to labeled acyclic digraphs.
iii. No two Boolen algebras with a atom are isomorphic.
iv. Non-zero elements of finite Boolean algebras are not uniquely expressible as joins of atoms.
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The relation ≤ and < on a boolean algebra are defined as:
x ≤ y if and only if x v y = y
x < y means x ≤ y but x ≠ y
x ≥ y means y ≤ x and
x > y means y < x
Considering the above definitions, which of the following is not true in the Boolean algebra?
i. If x ≤ y and y ≤ z, then x ≤ z
ii. If x ≤ y and y ≤ x, then x = y
iii. If x < y and y < z, then x ≤ y
iv. If x < y and y < z, then x < y
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