Advertisements
Advertisements
Question
Using truth table show that ∼ (p → ∼ q) ≡ p ∧ q
Advertisements
Solution
∼ (P → ∼ q) ≅ P ∧ q
=`(e^x/(2e^y))=1/2[e^(x-y)]`
`dy/dx=1/2[e^x+e^y]`
Truth table
| P (1) | q(2) | ∼q(3) | p→∼q (4) | ∼(p→∼q)(5) | p^q(6) |
| T | T | F | F | T | T |
| T | F | T | T | F | F |
| F | T | F | T | F | F |
| F | F | T | T | F | F |
From the truth table, we get 5th and 6th columns are
identical
∴∼(p→∼q)≅ p∧q
APPEARS IN
RELATED QUESTIONS
The side of an equilateral triangle is increasing at the rate of 2 cm/s. At what rate is its area increasing when the side of the triangle is 20 cm ?
Show that the function given by f(x) = sin x is
- strictly increasing in `(0, pi/2)`
- strictly decreasing in `(pi/2, pi)`
- neither increasing nor decreasing in (0, π)
Find the intervals in which the following functions are strictly increasing or decreasing:
x2 + 2x − 5
Prove that y = `(4sin theta)/(2 + cos theta) - theta` is an increasing function of θ in `[0, pi/2]`
Show that the function f(x) = 4x3 - 18x2 + 27x - 7 is always increasing on R.
Prove that the function f(x) = x3 − 6x2 + 12x − 18 is increasing on R ?
Write the set of values of a for which the function f(x) = ax + b is decreasing for all x ∈ R ?
Every invertible function is
Find the intervals in which the function `f("x") = (4sin"x")/(2+cos"x") -"x";0≤"x"≤2pi` is strictly increasing or strictly decreasing.
Let f(x) = x3 − 6x2 + 9𝑥 + 18, then f(x) is strictly decreasing in ______
Find the values of x for which f(x) = 2x3 – 15x2 – 144x – 7 is
- Strictly increasing
- strictly decreasing
The price P for the demand D is given as P = 183 + 120D − 3D2, then the value of D for which price is increasing, is ______.
Let f be a real valued function defined on (0, 1) ∪ (2, 4) such that f '(x) = 0 for every x, then ____________.
The interval in which the function f is given by f(x) = x2 e-x is strictly increasing, is: ____________.
Let `"f (x) = x – cos x, x" in "R"`, then f is ____________.
In `(0, pi/2),` the function f (x) = `"x"/"sin x"` is ____________.
The function f(x) = tan-1 (sin x + cos x) is an increasing function in:
The function `"f"("x") = "x"/"logx"` increases on the interval
State whether the following statement is true or false.
If f'(x) > 0 for all x ∈ (a, b) then f(x) is decreasing function in the interval (a, b).
Find the interval in which the function f(x) = x2e–x is strictly increasing or decreasing.
