Exercise 30.2
Page no 30.15
Type 1
Question 1
Write down the conjunction and disjunction of the following statements:
(i) $p:$ Jack went up the hill.
$q$ : Jill went up the hill.
(ii) $p:$ it is raining.
$q: 2$ is a prime number.
(iii) $p:$ Delhi is in India.
$4: 2+3=6$
(iv) $p:$ India is in Asia.
$q: 2+2=4$
(v) $p:$ Paris is in France.
$q$ : London is in England.
(vi) $p:$ it is raining today.
$q$ : There are twenty chairs in this room.
(vii) $p:$ Ram is a boy.
$q$ : Sita is a girl.
(viii) $p:$ It is not raining.
$q$ : It is hot.
(ix) $p$ : The sun shines.
$q:$ It rains:
(x) $p:$ Delhi is in India.
$q: 2+3=5$.
(xi) $p:$ Rajeev is rich.
$q$ : Rajeev is happy.
Question 2
Write down the following compound statements in symbolic forms:
(i) Paris is in France and London is in England.
(ii) Javed reads 'paper $\mathrm{X}$ or paper $\mathrm{Y}$ :'
(iii) Ram in in class XI or Rahim is in class X.
Type 2
Question 3
Write the negation of the following statements :
(i) I went to my class yesterday.
(ii) Complex numbers are real numbers.
(iii) All triangles are squares.
(iv) All natural numbers are integers.
(v) Every rational number is a real number.
(vi) $2+5=8$
(vii) There are twenty chairs in this room.
(viii) It is raining today.
Question 4
Write the negation of the following statements :
(i) Paris is in France and London is in England.
(ii) $x>8$ or $x<8$.
(iii) Rekha is smart or beautiful.
(iv) 8 is greater than 5 or 4 is less than 10 .
(v) Sky is blue and $5<8$.
(vi) I like tennis and football.
Question 5
Write all of the following statements in symbolic form as negative of statement.
(i) It is false that all natural numbers are integers.
(ii) It is not the case that all triangles are squares.
(iii) Not all real numbers are complex numbers.
(iv) There is an integer which is not a natural number.
(v) Some mathematicians are not men.
Question 6
Are the following statements negation of each other?
(i) " $r$ is not a rational number,"
${ }^{*} x$ is an irrational number."
(ii) " $x>10^{+}$and " $x \leq 10^{\circ}$, ( $x$ being a real number)
Type 3
Question 7
1. Write the truth value of the negation of the following statements :
(i) The earth is a star.
(ii) 12 is a prime number.
(iii) $2+3<4$.
(iv) Every square is a rectangle.
(v) Equilateral triangle is an isosceles triangle.
Type 4
Question 8
State the truth value of each of the following compound statement :
(i) India is in Europe or $2+2=5$.
(ii) India is in Asia or $2+2=4$.
(iii) $\sqrt{3}$ is an irrational number or 10 is divisible by 3 .
(iv) Delhi is in India and $2+3=6$.
(v) Taj Mahal is in Delhi or 2 is an even number.
(vi) Delhi is in England and zero is a purely imaginary number.
(vii) 29 is a prime number and a quadratic equation has only two roots.
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