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Mathematics
Mathematical statement
Which of the contrapositive of “If you understand logic, you will be a good consumer”
Option A: If you are a good consumer, then you do not understand logic.
Option B: If you are not a good consumer, then you do not understand logic.
Option C: If you do not understand logic, then you will not be a good consumer.
Option D: None of these

Mathematics
Mathematical statement
What is true about the statement “If two angles are right angles, the angles have equal measure” and its converse “If two angles have equal measure then the two angles are right angles”?
(A) The statement is true but its converse is false
(B) The statement is false but its converse is true
(C) Both the statement and its converse are false
(D) Both the statement and its converse are true

Mathematics
Mathematical statement
Which of the following statements is the inverse of “If it rains, then I do not go fishing”?
(A) If I go fishing, then it does not rain
(B) If I do not go fishing, then it rains
(C) If it does not rain, then I go fishing
(D) None of these
Mathematics
Mathematical statement
Which of the following statements is the converse of the “ if the moon is full then the vampires are prowling”.
A.If the vampires are prowling, then the moon is full.
B.If the moon is not full, then the vampires are not prowling.
C.If the vampires are not prowling, then the moon is not full.
D.None.

Mathematics
Mathematical statement
"If A is true, then B is false", is logically equivalent to which of the following?
I. If A is false, then B is true.
II. If B is false, then A is true.
III. If B is true, then A is false
\[A)\]None of the above
\[B)\]III only
\[C)\]I and II only
\[D)\]II and III only
$E)$I, II, and III

Mathematics
Mathematical statement
How many people watched the film Devdas, in PVR today?
I.In the show $80\% $of the PVR seats were occupied.
II.The number of people who watched each of the $4$shows today is in arithmetic progression.

I.If the question can be answered by anyone of the statement alone, but cannot be answered by using the other statement alone.
II.If the question can be answered by using either statement alone.
III.If the question can be answered by using both the statements together, but cannot be answered by using either statement alone.
IV.If the question cannot be answered even by using both the statements together.

Mathematics
Mathematical statement
Let p: If x is an integer and \[{{x}^{2}}\]is even, then x is even. Using the method of contrapositive, prove that p is true.

Mathematics
Mathematical statement
Match the following logical expression to its equivalent expression: $ (\neg (p \vee q)) \vee (\neg p \wedge q) $
(a) $ p $
(b) $ q $
(c) $ \neg p $
(d) $ \neg q $

Mathematics
Mathematical statement
Which of the following are statements?
1. May God bless you.
2. Mango is a flower.
3. Sugar is sweet.
4. 2 is a prime number.
A. (1),(2),(3)
B. (1),(2),(4)
C. (1),(3),(4)
D. (2),(3),(4)
Mathematics
Mathematical statement
Let p and q be two propositions. Then the contrapositive the implication \[p \to q\]
A. \[ \sim q \to \sim p\]
B. \[ \sim p \to \sim q\]
C. \[q \to p\]
D. \[p \leftrightarrow q\]
Mathematics
Mathematical statement
The conjunction of statements: “Roses are red and violets are blue.”
A. Roses are red and violets are blue.
B. Roses are red or violets are blue.
C. If roses are red, violets are blue.
D. Roses are red, only if violets are blue.

Mathematics
Mathematical statement
Negation of “Ram is in class X or Rashmi is in class XII” is
A.Ram is not in class X but Rashmi is in class XII
B.Ram is not in class X and Rashmi is not in class XII
C.Either Ram is not in class X or Rashmi is not in class XII
D.None of the above

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