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HSC Commerce (English Medium) १२ वीं कक्षा - Maharashtra State Board Question Bank Solutions

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Let p : Sachin wins the match.
q : Sachin is a member of Rajya Sabha.
r : Sachin is happy.
Write the verbal statement of the following.

p → r

[1] Mathematical Logic
Chapter: [1] Mathematical Logic
Concept: undefined >> undefined

Let p : Sachin wins the match.
q : Sachin is a member of Rajya Sabha.
r : Sachin is happy.
Write the verbal statement of the following.

∼ p ∨ q

[1] Mathematical Logic
Chapter: [1] Mathematical Logic
Concept: undefined >> undefined

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Let p : Sachin wins the match.
q : Sachin is a member of Rajya Sabha.
r : Sachin is happy.
Write the verbal statement of the following.
p→(q ∨ r)

[1] Mathematical Logic
Chapter: [1] Mathematical Logic
Concept: undefined >> undefined

Let p : Sachin wins the match.
q : Sachin is a member of Rajya Sabha.
r : Sachin is happy.
Write the verbal statement of the following.

p → q

[1] Mathematical Logic
Chapter: [1] Mathematical Logic
Concept: undefined >> undefined

Let p : Sachin wins the match.
q : Sachin is a member of Rajya Sabha.
r : Sachin is happy.
Write the verbal statement of the following.

(p ∧ q) ∧ ∼ r

[1] Mathematical Logic
Chapter: [1] Mathematical Logic
Concept: undefined >> undefined

Let p : Sachin wins the match.
q : Sachin is a member of Rajya Sabha.
r : Sachin is happy.
Write the verbal statement of the following.

∼ (p ∨ q) ∧ r

[1] Mathematical Logic
Chapter: [1] Mathematical Logic
Concept: undefined >> undefined

Rewrite the following statement without using conditional –
(Hint : p → q ≡ ∼ p ∨ q)

If price increases, then demand falls.

[1] Mathematical Logic
Chapter: [1] Mathematical Logic
Concept: undefined >> undefined

Rewrite the following statement without using conditional –
(Hint : p → q ≡ ∼ p ∨ q)

If demand falls, then price does not increase.

[1] Mathematical Logic
Chapter: [1] Mathematical Logic
Concept: undefined >> undefined

Write the negation of the following.

If ∆ABC is not equilateral, then it is not equiangular.

[1] Mathematical Logic
Chapter: [1] Mathematical Logic
Concept: undefined >> undefined

Write the negation of the following.

Ramesh is intelligent and he is hard working.

[1] Mathematical Logic
Chapter: [1] Mathematical Logic
Concept: undefined >> undefined

Write the negation of the following.

An angle is a right angle if and only if it is of measure 90°.

[1] Mathematical Logic
Chapter: [1] Mathematical Logic
Concept: undefined >> undefined

Write the negation of the following.

Kanchanganga is in India and Everest is in Nepal.

[1] Mathematical Logic
Chapter: [1] Mathematical Logic
Concept: undefined >> undefined

Write the negation of the following.

If x ∈ A ∩ B, then x ∈ A and x ∈ B.

[1] Mathematical Logic
Chapter: [1] Mathematical Logic
Concept: undefined >> undefined

Assuming the following statement.

p : Stock prices are high.

q : Stocks are rising.

to be true, find the truth value of the following.

Stock prices are high or stocks are not rising iff stocks are rising.

[1] Mathematical Logic
Chapter: [1] Mathematical Logic
Concept: undefined >> undefined

Determine the order and degree of the following differential equations.

`(d^2x)/(dt^2)+((dx)/(dt))^2 + 8=0`

[8] Differential Equation and Applications
Chapter: [8] Differential Equation and Applications
Concept: undefined >> undefined

Determine the order and degree of the following differential equations.

`((d^2y)/(dx^2))^2 + ((dy)/(dx))^2 =a^x `

[8] Differential Equation and Applications
Chapter: [8] Differential Equation and Applications
Concept: undefined >> undefined

Determine the order and degree of the following differential equations.

`(d^4y)/dx^4 + [1+(dy/dx)^2]^3 = 0`

[8] Differential Equation and Applications
Chapter: [8] Differential Equation and Applications
Concept: undefined >> undefined

Determine the order and degree of the following differential equations.

`(y''')^2 + 2(y'')^2 + 6y' + 7y = 0`

[8] Differential Equation and Applications
Chapter: [8] Differential Equation and Applications
Concept: undefined >> undefined

Determine the order and degree of the following differential equations.

`sqrt(1+1/(dy/dx)^2) = (dy/dx)^(3/2)`

[8] Differential Equation and Applications
Chapter: [8] Differential Equation and Applications
Concept: undefined >> undefined

Determine the order and degree of the following differential equations.

`dy/dx = 7 (d^2y)/dx^2`

[8] Differential Equation and Applications
Chapter: [8] Differential Equation and Applications
Concept: undefined >> undefined
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