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MATHEMATICAL REASONING PART 4
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 logically equivalent to (p ^ q)?
p → q
̴ p ^ ̴ q
p ^ ̴ q
̴ (p → ̴ q)
3.
The contra positive of 2x + 3 = 9 => x ≠ 4 is
x= 4 => 2x +3 ≠9
x= 4 => 2x +3 =9
x ≠ 4 => 2x +3 ≠9
x ≠ 4 => 2x +3 =9
4.
The proposition ( p → ̴ p ) ^ ( ̴ p →p ) is a
Tautology
Contradiction
Neither a tautology nor a contradiction
Tautology and contradiction
5.
Consider the following statements p : I shall pass q: I study The symbolic representation of the proposition “ I shall Pass iff I study” is
p→ q
q→ p
p→ ̴ q
p↔ q
6.
The proposition p → ̴ ( p ^ ̴ q) is
A contradiction
a tautology
either a tautology or a contradiction
neither a tautology nor a contradiction
7.
̴ ( p ˅ q ) ˅ ( ̴ p ^ q ) is logically equivalent to
~p
p
q
~q
8.
The negation of the compound proposition p ˅ ( ̴ p ˅ q) is ?
( p ^ ̴ q) ^ ̴ p
( p ^ ̴ q) ˅ ̴ p
( p ^ ̴ q) ˅ ̴ q
None of these
9.
Let p be the proposition : mathematics is interesting And let q be the proposition that mathematics is difficult then the symbol p ^ q means?
Mathematics Is interesting implies that mathematics is difficult
Mathematics Is interesting implies and is implied by Mathematics is difficult
Mathematics is interesting and Mathematics is difficult
Mathematics is interesting or Mathematics is difficult
10.
The inverse of the proposition ( p ^ ̴ q ) → r is
̴ r → ̴ p ˅ q
̴ p ˅ q → ̴ r
r → p ^ ̴ q
None of these
Answers
1 -> D
2 -> D
3 -> A
4 -> B
5 -> D
6 -> D
7 -> A
8 -> A
9 -> C
10 -> B