Utilizing ISC Mathematics Class 11 OP Malhotra Solutions Chapter 27 Mathematical Reasoning Ex 27(e) as a study aid can enhance exam preparation.
S Chand Class 11 ICSE Maths Solutions Chapter 27 Mathematical Reasoning Ex 27(e)
Question 1.
Write each sentence in the “If ……….. then” form.
(i) Roses are vegetables if carrots are flowers.
(ii) All ducks are birds.
(iii) Vertical angles are equal.
(iv) Freezing water expands.
(v) A set with no elements is called the empty set.
(vi) A racer wins the race only if he runs fast.
(vii) Any two parallel lines are coplanar.
Solution:
(i) If carrots are flowers then roses are vegetables.
(ii) If the creature is a duck then it is a bird.
(iii) If two angles are vertical angles then they are equal.
(iv) If the water is freezing then it expands.
(v) If the set has no element then it is called the empty set.
(vi) If the racer runs fast then the racer wins the race.
(vii) If two lines are parallel then they are coplanar.
Question 2.
Let p be “I will marry her,” and let q be “she is beautiful.” Translate into symbolic form.
(i) If she is beautiful, then I will marry her.
(ii) If I will marry her, then she is beautiful.
(iii) If I will marry her, then she is beautiful.
(iv) If she is not beautiful, then I will not marry her.
(v) If I will not marry her, then she is not beautiful.
(vi) If she is beautiful, then I will not marry her.
Solution:
Given statements are ;
p : I will marry her
q : she is beautiful
(i) q ⇒ p
(ii) p ⇒ q
(iii) q ⇔ p
(iv) ~q ⇒ ~p
(v) ~p ⇒ ~ q
(vi) q ⇒ ~p
Question 3.
Determine whether p, q and ‘If p, then q’ are true or false in each case given below :
| (i) 3 is a prime number | 3 is an even number |
| (ii) 5 <7 | 5 is odd |
| (iii) 3 > 2 | 2 × 7 = 14 |
| (iv) 1 > 4 | 2 is even |
| (v) 5 × 3 = 16 | 2 + 7 = 6 |
| (vi) 3 (5 ÷ 6) < 1 | 8 – 3 ÷ 6 > 9 |
Solution:
(i) Given p : 3 is a prime number (True)
q : 3 is an even number (False)
Then p ⇒ q is false
(ii) p : 5 < 7 (True) q : 5 is odd (True) Then p ⇒ q is true (iii) p : 3 > 2 (True)
q : 2 × 7 = 14 (True)
Then p ⇒ q is true.
(iv) p : 1 > 5 (False)
q : 2 is even (True)
Then p ⇒ q is true
(v) p : 5 × 3 = 16 (False)
q : 2 + 7 = 6 (False)
Then p ⇒ q is true
(vi) p : 3 (5 ÷ 6) < 1 (False) q : 8 – 3 ÷ 6 > 9 (False)
Then p ⇒ q is true.
Question 4.
Write T before each true statement and write F before each false statement. Then give the truth value of the conditional expressed.
(i) If Asia is a continent, then Delhi is in Japan.
(ii) If monkeys climb trees, then 6 is divisible by 2.
(iii) If oxygen is a gas, then gold is a compound.
(iv) Water is dry ⇒ show is hot.
(v) Show is cold ⇒ water is wet.
(vi) If 3 = 5, then 7 is a prime number.
(vii) 5 × 6 – 4 = 21 ⇒ 2 (5 ÷ 15 + 3) = \(\frac { 20 }{ 3 }\).
(viii) If a triangle is a rectangle, then a circle is a rhombus.
(ix) If 51 is the product of + 17 and – 3, then lions can fly in the air.
(x) If √5 is an integer, then 3 is an integer.
Solution:
(i) Let p : Asia is a continent (T)
q : Delhi is in Japan (F)
Then p ⇒ q is false (F)
(ii) Let p : Monkeys climb Trees (T)
q : 6 is divisible by 2 (T)
Then given statement p
⇒ q is True (T)
(iii) Let p : Oxygen is a gas (T)
q : Gold is a compound (F)
Then given statement p
⇒ q is false (F)
(iv) Let p : water is dry (F)
q : snow is hot (F)
Then p ⇒ q is true (T)
(v) Let p : Snow is cold (T)
and q : water is wet (T)
Then p ⇒ q is True (T)
(vi) Let p : 3 = 5 (F)
q : 7 is a prime number (T)
Then p ⇒ q is True (T)
(vii) Let p : 5 × 6 – 4 = 21 (F)
q : 2(5 ÷ 15 + 3) = 2 \(\left(\frac{1}{3}+3\right)\) = \(\frac { 20 }{ 3 }\) (T)
Then p ⇒ q is true
(viii) Let p : triangle is a rectangle (F)
q : Circle is a rhombus (F)
Then p ⇒ q is true (T)
(ix) Let p : 51 is the product of + 17 and (-3) (F)
q : lions can fly in the air (F)
Then p ⇒ q is true (T)
(x) Let P : √5 is an integer (F)
q : 3 is an integer (T)
Then p ⇒ q is true (T)