Mathematical Reasoning OP Malhotra Class-11 S.Chand ISC Maths Solution Chapter-27. Step by step Solutions of OP Malhotra S.Chand ISC Class-11 Mathematics with Exe-27 (a), 27 (b), 27 (c), 27 (d), 27 (e), 27 (f), 27 (g), With Chapter Test. Visit official Website CISCE for detail information about ISC Board Class-12 Mathematics.
Mathematical Reasoning OP Malhotra Class-11 S.Chand ISC Maths Solution
| Class: | 11th |
| Subject: | Mathematics |
| Chapter : | Ch-27 Mathematical Reasoning of Section -B |
| Board | ISC |
| Writer | OP Malhotra |
| Publications | S.Chand Publications 2020-21 |
–: Select Topics :-
Mathematical Reasoning OP Malhotra Class-11 S.Chand ISC Maths Solution
Simple Statements
A statement is called simple if it cannot be broken down into two or more statements.
Compound Statements
A compound statement is the one which is made up of two or more simple statement.
Connectives
The words which combine or change simple statements to form new statements or compound statements are called connectives.
Conjunction
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 of p and q is written in symbolic form as “p ∧ q”.
Note:
- The statement p ∧ q has the truth value T (true) whenever both p and q have the truth value T.
- The statement p ∧ q has the truth value F (false) whenever either p or q or both have the truth value F.
Disjunction
If two simple statements p and q are connected by the word ‘or’, then the resulting compound statement “p or q” is called disjunction of p and q and is written in symbolic form as “p ∨ q”.
Note:
- The statement p ∨ q has the truth value F whenever both p and q have the truth value F.
- The statement p ∨ q has the truth value T whenever either p or q or both have the truth value T.
Negation
An assertion that a statement fails or denial of a statement is called the negation of the statement. The negation of a statement p in symbolic form is written as “~p”.
Note:
- ~p has truth value T whenever p has truth value F.
- ~p has truth value F whenever p has truth value T.
The Conditional Statement
If p and q are any two statements, then the compound statement “if p then g” formed by joining p and q by a connective ‘if-then’ is called a conditional statement or an implication and is written in symbolically p → q or p ⇒ q, here p is called hypothesis (or antecedent) and q is called conclusion (or consequent) of the conditional statement (p ⇒ q).
Contrapositive of Conditional Statement
The statement “(~q) → (~p) ” is called the contrapositive of the statement p → q.
The Biconditional Statement
If two statements p and q are connected by the connective ‘if and only if’, then the resulting compound statement “p if and only if q” is called biconditional of p and q and is written in symbolic form as p ⇔ q.
Quantifier
(i) For all or for every is called universal quantifier.
(ii) There exists is called existential quantifier.
Exe-27 (a)
OP Malhotra Class-11 Mathematical Reasoning S.Chand ISC Maths Solution
Page 27-3
In the following problems, determine if the …………………. give the components.
Question 1:
Open the door.
…………………
………………….
………………….
Question 16:
3 + 4i is a complex number.
Exe-27 (b)
OP Malhotra Class-11 Mathematical Reasoning S.Chand ISC Maths Solution
Page 27-4
Question 1:
Identity the ………… statements.
(i)……….
(ii)………..
(iii)………..
Question 2:
Symbolize the following statement :
……………..
………………
Exe-27 (c)
OP Malhotra Class-11 Mathematical Reasoning S.Chand ISC Maths Solution
Page 27-7 to 27-8
Question 1:
Write the given statement ……………….. component.
(i)……………..
(ii)…………….
…………………
Question 2:
………………..
…………………
…………………
Question 5:
Give the negaative of each of following statements
(i)………..
(ii)……….
(iii)………..
……………..
Exe-27 (d)
Mathematical Reasoning OP Malhotra Class-11 S.Chand ISC Maths Solution
Page 27- 13
Question 1:
Let p, q, r, and s represent ……………… expressed below.
……………….
Question 2:
……………………
…………………….
……………………
Question 14:
Let p be ……………. 165 cm tall.
(i)………….
……………..
Exe-27 (e)
Class-11 Mathematical Reasoning S.Chand ISC Maths Solution
Page 27- 18
Question 1:
Write each sentence in the ………….. form
(i) Roses are …………..
(ii)………..
……………….
Question 2:
……………………
……………………
Question 4:
Write T before each true statement …………….. condition expressed
(i) If Asia is a …………..
(ii) If monkey climb …………
…………………
Exe-27 (f)
Mathematical Reasoning OP Malhotra Class-11 S.Chand ISC Maths Solution
Page 27- 23 to 27-24
Question 1:
Write the ………………… statement .
(i) if you do not ………..
(ii) if you drink ………….
(iii) you will be …………..
Question 2:
…………………..
…………………..
…………………..
Question 13:
If p and q are any …………………….. is bolid ?
……………..
…………………
Exe-27 (g)
Class-11 Mathematical Reasoning S.Chand ISC Maths Solution
Page 27- 27
Question 1:
Show that the statement ……………………. is turly.
(i) ………..
(ii)………….
(iii)…………
Question 2:
…………………….
……………………
…………………….
Question 5:
Verify by the method of ………………. is irrational.
Chapter Test
Mathematical Reasoning OP Malhotra Class-11 S.Chand ISC Maths Solution
Page 27- 29
Question 1:
For each of the following ………………………. component statements
Question 2:
………………………
………………………
……………………….
Question 6 :
Write the following …………………. A and B are equal :
-: End of Mathematical Reasoning Solution :
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