Mathematical Reasoning MCQ Questions & Answers in Algebra | Maths
Learn Mathematical Reasoning MCQ questions & answers in Algebra are available for students perparing for IIT-JEE and engineering Enternace exam.
11.
The contrapositive of the statement, ' If I do not secure good marks then I cannot go for engineering', is
A
If I secure good marks, then I go for engineering
B
If I go for engineering then I secure good marks
C
If I cannot go for engineering then I donot secure good marks
D
None
Answer :
If I go for engineering then I secure good marks
The contra positive of the given statement is ‘If I go for engineering then I secure good marks’
12.
Which of the following is not a proposition
A
$$\sqrt 3 \,$$ is a prime
B
$$\sqrt 2\, $$ is irrational
C
Mathematics is interesting
D
5 is an even integer
Answer :
Mathematics is interesting
Mathematics is interesting is not a logical sentence. It may be interesting for some persons are may not be interesting for others.
$$\therefore $$ This is not a propositions.
13.
The negation of the statement $$\left( {p \wedge q} \right) \to \left( { \sim p \vee r} \right){\text{is}}$$
14.
The negation of the statement “A circle is an ellipse” is
A
an ellipse is a circle
B
an ellipse is not a circle
C
a circle is not an ellipse
D
a circle is an ellipse
Answer :
a circle is not an ellipse
The negation of statement “A circle is an ellipse” is “A circle is not an ellipse”.
15.
The Boolean expression $$ \sim \left( {p \vee q} \right) \vee \left( { \sim p \wedge q} \right)$$ is equivalent to:
A
$$p$$
B
$$q$$
C
$$ \sim q$$
D
$$ \sim p$$
Answer :
$$ \sim p$$
$$\eqalign{
& \sim \left( {p \vee q} \right) \vee \left( { \sim p \wedge q} \right) \cr
& \left( { \sim p \wedge \sim q} \right) \vee \left( { \sim p \wedge q} \right) \cr
& \Rightarrow \,\, \sim p \wedge \left( { \sim q \vee q} \right) \cr
& \Rightarrow \,\, \sim p \wedge t \equiv \, \sim p \cr} $$
16.
If $$p$$ is false and $$q$$ is true, then
A
$$p \wedge q$$ is true
B
$$p \vee \sim q$$ is true
C
$$q \wedge p$$ is true
D
$$p \Rightarrow q$$ is true
Answer :
$$p \Rightarrow q$$ is true
When $$p$$ is false and $$q$$ is true, then $$p \wedge q$$ is false, $$p \vee \sim q$$ is false. ($$\because $$ both $$p$$ and $$ \sim q$$ are false)
and $$q \Rightarrow p$$ is also false,
only $$p \Rightarrow q$$ is true.
17.
Consider the following statements
$$p :$$ A tumbler is half empty.
$$q :$$ A tumbler is half full.
Then, the combination form of “$$p$$ if and only if $$q\,$$” is
A
a tumbler is half empty and half full
B
a tumbler is half empty if and only if it is half full
C
Both $$\left( A \right){\text{ and }}\left( B \right)$$
D
None of the above
Answer :
a tumbler is half empty if and only if it is half full
The given statements are
$$p :\,$$ A tumbler is half empty.
$$q :\,$$ A tumbler is half full.
We know that, if the first statement happens, then the second happens and also if the second happens, then the first happens. We can express this fact as
If a tumbler is half empty, then it is half full.
If a tumbler is half full, then it is half empty.
We combine these two statements and get the following. A tumbler is half empty, if and only if it is half full.
18.
If $$p :$$ It is snowing, $$q :$$ I am cold, then the compound statement "It is snowing and it is not that I am cold" is given by
A
$$p \wedge \left( { \sim p} \right)$$ is a contradiction
B
$$\left( {p \Rightarrow q} \right) \Leftrightarrow \left( { \sim q \Rightarrow \, \sim p} \right)$$ is a contradiction
C
$$ \sim \left( { \sim p} \right) \Leftrightarrow p$$ is a tautology
D
$$p \vee \left( { \sim p} \right) \Leftrightarrow p$$ is a tautology
Answer :
$$\left( {p \Rightarrow q} \right) \Leftrightarrow \left( { \sim q \Rightarrow \, \sim p} \right)$$ is a contradiction
$${p \Rightarrow q}$$ is logically equivalent to $${ \sim p \Rightarrow \, \sim q}$$
$$\therefore \left( {p \Rightarrow q} \right) \Leftrightarrow \left( { \sim q \Rightarrow \, \sim p} \right)\,$$ is a tautology but not a contradiction.