Mathematical Reasoning Class 11 OP Malhotra Exe-27E ISC Maths Ch-27 Solutions. In this article you would learn about Truth Table For A Conditional. Step by step solutions of latest textbook has been given as latest syllabus. Visit official Website CISCE for detail information about ISC Board Class-11 Mathematics.

Mathematical Reasoning Class 11 OP Malhotra Exe-27E ISC Maths Solutions Ch-27

Board	ISC
Publications	S Chand
Subject	Maths
Class	11th
Chapter-27	Mathematical Reasoning
Writer	O.P. Malhotra
Exe-27(E)	Truth Table For A Conditional

Truth Table For A Conditional.

Mathematical Reasoning Class 11 OP Malhotra Exe-27E ISC Maths Ch-27 Solutions.

Que-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.

Sol: (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.

Que-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.

Sol: 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

Que-3: Determine whether p, q and ‘If p, then q’ are true or false in each case given below :

Sol: (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.

Que-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) = 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.

Sol: (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 ((1/3)+3) = 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)

–: End of Mathematical Reasoning Class 11 OP Malhotra Exe-27E ISC Maths Ch-27 Solutions. :–

Return to :- OP Malhotra ISC Class-11 S Chand Publication Maths Solutions

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