20 questions · self-marked practice — reveal the answer and mark yourself.
The negation of the statement.
“7 is greater than 8” is.
Solution:
Let p: 7 is greater than 8.
~p: 7 is not greater than 8.
Which of the following statement is a conjunction?
Solution:
If two simple statements p and q are connected by the word ‘and’, then the resulting compound statement p and q is called a conjunction ofp and q. Here, none of the given statement is conjunction.
The converse of the statement.
“If sun is not shining, then sky is filled with clouds” is.
Solution:
Let p: Sun is not shining.
q: Sky is filled with clouds.
So, the converse of the statement p → q is q → p.
i.e., If Sky is filled with clouds, then the Sun is not shining.
The connective in the statement.
“Earth revolves round the Sun and Moon is a satellite of earth” is.
Solution:
Connective word is “and”.
The negation of the statement.
“Plants take in CO2 and give out O2 ” is.
Solution:
Let p: Plants take in CO2 and give out O2.
q: Plants take in CO2.
r: Plants give out O2
~q: Plants do not take in CO2.
~r: Plants do not give out O2.
$\therefore$ ~(q ^ r) = (~q ~r): plants do not take in CO2 or do not give out O2.
The contrapositive of statement ‘If Chandigarh is capital of Punjab, then Chandigarh is in India’ is.
Solution:
Let p: Chandigarh is capital of Punjab.
and q: Chandigarh is in India.
~p: Chandigarh is not capital of Punjab.
~q: Chandigarh is not in India.
Contra positive of the statement p → q
if (~q), then (~p).
It Chandigarh is not in India, then Chandigarh is not the capital of Punjab.
The negation of the statement “The product of 3 and 4 is 9” is.
Solution:
The negation of the statement is “It is false that the product of 3 and 4 is 9”.
The connective in the statement.
“2 + 7 > 9 or 2 + 7 < 9” is
Solution:
In ‘2 + 7 > 9 or 2 + 7 < 9’ the connective is ‘or’.
Which of the following is a statement.
Solution:
Since, statement is a sentence which is ether true or false. So, 6 is a natural number which is true.
The converse of the statement.
“If x > y, then x + a > y + a” is.
Solution:
Let p: x > y
q: x + a > y + a
P ⟶ q
Converse of the above statement is:
q ⟶ P
i.e., If x + a > y + a, then x > y
The contrapositive of the statement.
“If 7 is greater than 5, then 8 is greater than 6” is.
Solution:
Letp: 7 is greater than 5.
and q: 8 is greater than 6.
$\therefore $ p → q
~p: 7 is not greater than 5.
~q: 8 is not greater than 6.
(~q) → (~p) i.e., if 8 is not greater than 6, then 7 is not greater than 5.
The negation of the statement.
“72 is divisible by 2 and 3” is.
Solution:
We have, p: 72 is divisible by 2 and 3.
Let q: 72 is divisible by 2.
r: 72 is divisible by 3.
~q: 72 is not divisible by 2.
~r. 72 is not divisible by 3.
~{q ⋀ f ) -~q v ~r
⟹ 72 is not divisible by 2 or 72 is not divisible by 3.
The negation of the statement.
“101 is not a multiple of 3” is.
Solution:
Let p: 101 is not multiple of 3.
~p: 101 is a multiple of 3.
Which of the following is the conditional p → q?
Solution:
We know that p → q is same as p only if q.
The statement “If x2 is not even, then x is not even” is converse of the statement.
Solution:
Let p: x2 is not even.
q: x is not even. So, the converse of the statement p → q is q → p
i.e., If x is not even, then x2 is not even.
The contrapositive of the statement.
“If p, then q”, is.
Solution:
p → q
If p, then q
Contra positive of the statement p → q is (~q) →(~p).
If ~q, then ~p.
Which of the following is not a negation of “A natural number is greater than zero”.
Solution:
The negation of the given statement is false. i.e., It is false that a natural number is not greater than zero.
The negation of the statement.
“Rajesh or Rajni lived in Bangalore” is.
Solution:
We have, p: Rajesh or Rajni lived in Bangalore.
and q: Rajesh lived in Bangalore.
r: Rajni lived in Bangalore.
~q: Rajesh did not live in Bangalore.
~r. Rajni did not live in Bangalore.
~ (q v r): Rajesh did not live in Bangalore and Rajni did not live in Bangalore.
The negation of the statement.
“A circle is an ellipse” is.
Solution:
Let p: A circle is an ellipse.
~p: A circle is not an ellipse.
Which of the following is not a statement.
Solution:
To given order cannot be a statement. So ‘Come here’ is not a statement.