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Chapters
1.2: Matrics
1.3: Trigonometric Functions
1.4: Pair of Lines
1.5: Vectors and Three Dimensional Geometry
1.6: Line and Plane
1.7: Linear Programming Problems
2.1: Differentiation
2.2: Applications of Derivatives
2.3: Indefinite Integration
2.4: Definite Integration
2.5: Application of Definite Integration
2.6: Differential Equations
2.7: Probability Distributions
2.8: Binomial Distribution
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Solutions for Chapter 1.1: Mathematical Logic
Below listed, you can find solutions for Chapter 1.1 of Maharashtra State Board SCERT Maharashtra for Mathematics and Statistics (Arts and Science) [English] 12 Standard HSC.
SCERT Maharashtra solutions for Mathematics and Statistics (Arts and Science) [English] 12 Standard HSC 1.1 Mathematical Logic MCQ
2 Marks
Which of the following statement is true
3 + 7 = 4 or 3 – 7 = 4
If Pune is in Maharashtra, then Hyderabad is in Kerala
It is false that 12 is not divisible by 3
The square of any odd integer is even
Which of the following is not a statement?
Smoking is injuries to health
2 + 2 = 4
2 is the only even prime number.
Come here
If p is any statement then ( p ˅ ∼ p) is a
Contingency
Contradiction
Tautology
None of these
If p and q are two statements then (p → q) ↔ (∼ q → ∼ p) is ______.
Contradiction
Tautology
Neither (i) not (ii)
None of the these
Negation of p → (p ˅ ∼ q) is ______
∼ p → (∼ p ˅ q)
p ˄ (∼ p ˄ q)
∼ p ˅ (∼ p ˅ ∼ q)
∼ p → (∼ p → q)
Choose the correct alternative :
If p : He is intelligent.
q : He is strong
Then, symbolic form of statement “It is wrong that, he is intelligent or strong” is
∼ p ∨ ∼ p
∼ (p ∧ q)
∼ (p ∨ q)
p ∨ ∼ q
A biconditional statement is the conjunction of two ______ statements.
Negative
Compound
Connective
Conditional
If p → q is an implication, then the implication ∼ q → ∼ p is called its
Converse
Contrapositive
Inverse
Alternative
The negation of the statement (p ˄ q) `→` (r ˅ ∼ p) is ______.
p ˄ q ˄ ∼ r
(p ˄ q) ˅ r
p ˅ q ˅ ∼ r
(p v q) ˄ (r ˅ s)
The false statement in the following is ______.
p ˄ (∼ p) is contradiction
(p → q) ↔ (∼ q → ∼ p) is a contradiction
∼ (∼ p) ↔ p is a tautology
p ˅ (∼ p) ↔ p is a tautology
SCERT Maharashtra solutions for Mathematics and Statistics (Arts and Science) [English] 12 Standard HSC 1.1 Mathematical Logic Very Short Answers
1 mark
Find the negation of 10 + 20 = 30
State the truth Value of x2 = 25
Write the negation of p → q
State the truth value of `sqrt(3)` is not an irrational number
State the truth value of (p ˅ ∼p)
State the truth value of (p ˄ ∼p)
SCERT Maharashtra solutions for Mathematics and Statistics (Arts and Science) [English] 12 Standard HSC 1.1 Mathematical Logic Short Answers I
2 Marks
If statements p, q are true and r, s are false, determine the truth values of the following.
~ p ∧ (q ∨ ~ r)
If statements p, q are true and r, s are false, determine the truth values of the following.
(p ∧ ~r) ∧ (~q ∨ s)
Write the following compound statement symbolically.
Nagpur is in Maharashtra and Chennai is in Tamil Nadu.
Write the following compound statements symbolically.
Triangle is equilateral or isosceles
Write the converse and contrapositive of the following statements.
“If a function is differentiable then it is continuous”
Without using truth table prove that:
~ (p ∨ q) ∨ (~ p ∧ q) ≡ ~ p
SCERT Maharashtra solutions for Mathematics and Statistics (Arts and Science) [English] 12 Standard HSC 1.1 Mathematical Logic Long Answers II
4 marks
Write the negation of the statement “An angle is a right angle if and only if it is of measure 90°”
Write the following statements in symbolic form
Milk is white if and only if the sky is not blue
Write the following statements in symbolic form
If Kutab – Minar is in Delhi then Taj - Mahal is in Agra
Write the following statements in symbolic form
Even though it is not cloudy, it is still raining
Use quantifiers to convert the following open sentences defined on N, into a true statement.
n2 ≥ 1
Use quantifiers to convert the given open sentence defined on N into a true statement
3x – 4 < 9
Use quantifiers to convert the given open sentence defined on N into a true statement
Y + 4 > 6
Examine whether the following statement pattern is a tautology, a contradiction or a contingency.
(p ∧ ~ q) → (~ p ∧ ~ q)
Using truth table prove that ∼p ˄ q ≡ (p ˅ q) ˄ ∼p
Write the dual statement of the following compound statement.
13 is prime number and India is a democratic country.
Write the dual of the following
(p ˄ ∼q) ˅ (∼p ˄ q) ≡ (p ˅ q) ˄ ∼(p ˄ q)
Write the converse, inverse, and contrapositive of the following statement.
"If it snows, then they do not drive the car"
SCERT Maharashtra solutions for Mathematics and Statistics (Arts and Science) [English] 12 Standard HSC 1.1 Mathematical Logic Long Answers III
4 marks
Examine whether the statement pattern
[p → (∼q ˅ r)] ↔ ∼[p → (q → r)] is a tautology, contradiction or contingency.
Using truth table prove that p ˅ (q ˄ r) ≡ (p ˅ q) ˄ (p ˅ r)
Without using truth table show that -
(p ˅ q) ˄ (∼p v ∼q) ≡ (p ∧ ∼q) ˄ (∼p ∧ q)
With proper justification, state the negation of the following.
(p ↔ q) v (~ q → ~ r)
Prepare truth table for (p ˄ q) ˅ ~ r
(p ∧ q) ∨ ~ r
Solutions for 1.1: Mathematical Logic
SCERT Maharashtra solutions for Mathematics and Statistics (Arts and Science) [English] 12 Standard HSC chapter 1.1 - Mathematical Logic
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Concepts covered in Mathematics and Statistics (Arts and Science) [English] 12 Standard HSC chapter 1.1 Mathematical Logic are Concept of Statements, Truth Value of Statement, Logical Connective, Simple and Compound Statements, Statement Patterns and Logical Equivalence, Tautology, Contradiction, and Contingency, Duality, Quantifier and Quantified Statements in Logic, Negations of Compound Statements, Converse, Inverse, and Contrapositive, Algebra of Statements, Application of Logic to Switching Circuits.
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