And
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Q.
(p ∧∼q)∧(∼p ∧ q) is
A tautology
A fallacy
Both a tautology and a fallacy
Neither a tautology nor a fallacy
Q. OR is a logical disjunction and AND is a logical conjunction.
- False
- True
Q. Consider the following three statements:
p:4 and 7 are coprimes.
q: Every function on a set A is a relation on A.
r:6 divides 3.
Then the truth value of which of the following Boolean expressions is false?
p:4 and 7 are coprimes.
q: Every function on a set A is a relation on A.
r:6 divides 3.
Then the truth value of which of the following Boolean expressions is false?
- p∧(q∨r)
- ∼p∨(∼q ∨∼r)
- ∼p∧(q ∨∼r)
- (p ∨∼q)∨r
Q. Let
p:2 is a prime number
q:cos30∘=12
r:sec2x+tan2x=1
s:√7 is an irrational number
u:π2 is greater than 10
Then which among the following statements are valid
p:2 is a prime number
q:cos30∘=12
r:sec2x+tan2x=1
s:√7 is an irrational number
u:π2 is greater than 10
Then which among the following statements are valid
- p∨q, q∨s, r∨s, s∨u
- p∧q, q∧s, r∧s, s∧u
- p∨q, q∨r, r∨s, s∨u
- p∨q, q∧r, r∨s, s∧u
Q. The statement (p∨q)∧(∼p ∧∼q) is
- a contradiction
- a contingency
- logically equivalent to x∨(∼x)
- a tautology
Q. Let p:2 is a prime number
q:cos30∘=12
r:sec2x+tan2x=1
s:√7 is an irrational number
u:π2 is greater than 10
The statement which are all false is
q:cos30∘=12
r:sec2x+tan2x=1
s:√7 is an irrational number
u:π2 is greater than 10
The statement which are all false is
- p∨q, r∨s, r∨u
- p∧q, q∨r, p∨u
- p∧q, q∧s, s∧u
- p∧q, q∨r, r∨s
Q. The truth value of "20+10=2" and
"20×10=200" is
"20×10=200" is
- F
- T
- T or F based on sub statements truth value
- cannot be determined
Q. If p:x is odd; q:x2 is odd. Then "x is odd and x2 is not odd", is represented as
- p∧q
- (∼p)∨q
- p∧(∼q)
- p∨q
Q. Truth value for the statement "5+7=10 and 4+3=7" is
- Depends upon the truth values of sub statement.
- 5+7=10⟺4+3=7 can not be determined.
- T
- F
Q. The disjunction statement that can be formed from statements, " It is raining"; "The sun is shining", is
- It is raining and the sun is shining
- It is raining or the sun is shining
- It is raining and the sun is not shining
- It is not raining or the sun is not shining