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MATHEMATICAL REASONING PART 3
1.
Which of the following Is logically equivalent to ̴ ( ̴ p →q) ?
p ^ q
p ^ ̴ q
̴ p ^ q
̴ p ^ ̴ q
2.
Which of the following Is a contradiction ?
( p ^ q) ^ ( ̴ (p ˅ q )
p ˅ ( ̴ p ^ q )
(p → q)→p
None of these
3.
The negative of the proposition : "if a number is divisible By 15 then it is divisible by 5 or 3"
If a number is divisible by 15 and it is not divisible by 5 and 3
A number is divisible by 15 and it is not divisible by 5 and 3
A number is divisible by 15 and it is not divisible by 5 or 3
A number is not divisible by 15 or it is not divisible by 5 and 3
4.
~(~p)⟷p is
A tautology
A contradiction
Neither a contradiction nor a tautology
None of these
5.
Consider the proposition : “ if we control population growth, We prosper”. Negative of this proposition is
If we do not control population growth, we prosper
If we control population, we do not prosper
We control population but we do not prosper
We do not control population but we prosper
6.
The negation of q ˅ ̴ ( p ^ r) is
̴ q ˅ ̴ ( p ^ r)
̴ q ˅ ( p ^ r)
̴ q ^ ( p ^ r)
̴ q ^ ̴ ( p ^ r)
7.
The negation of p ^ ̴ ( q ^ r) is
̴ p ˅ ( q^ r)
̴ p ˅ ( ̴ q ˅ ̴ r)
p ˅ ( q^ r)
̴ p ^ ( q ˅ r)
8.
The contra positive of ( ̴ p^ q ) → ̴ r is
( p^ q) → r
( p ˅ q) → r
r→ ( p ˅ ̴ q)
None of these
9.
P → q Is logically equivalent to
p ^ ̴ q
̴ p → ̴ q
̴ q → ̴ p
None of these
10.
Which of the following is logically equivalent to ̴ ( p ↔ q) ?
( p ^ ̴ q) ^ ( q ^ ̴ p )
p ˅ q
( p ^ ̴ q) ˅ ( q ^ ̴ p )
None of these
Answers
1 -> D
2 -> A
3 -> B
4 -> A
5 -> C
6 -> C
7 -> A
8 -> C
9 -> C
10 -> C