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
Price P for demand D is given as P = 183 +120D - 3D2 Find D for which the price is increasing
Show that the function given by f(x) = 3x + 17 is strictly increasing on R.
Which of the following functions are strictly decreasing on `(0, pi/2)`?
- cos x
- cos 2x
- cos 3x
- tan x
On which of the following intervals is the function f given byf(x) = x100 + sin x –1 strictly decreasing?
Prove that the function f(x) = loge x is increasing on (0, ∞) ?
Find the interval in which the following function are increasing or decreasing \[f\left( x \right) = \left\{ x(x - 2) \right\}^2\] ?
Find the interval in which the following function are increasing or decreasing \[f\left( x \right) = \frac{3}{2} x^4 - 4 x^3 - 45 x^2 + 51\] ?
Show that f(x) = cos x is a decreasing function on (0, π), increasing in (−π, 0) and neither increasing nor decreasing in (−π, π) ?
Determine whether f(x) = −x/2 + sin x is increasing or decreasing on (−π/3, π/3) ?
Prove that the function f given by f(x) = x3 − 3x2 + 4x is strictly increasing on R ?
The edge of a cube is decreasing at the rate of`( 0.6"cm")/sec`. Find the rate at which its volume is decreasing, when the edge of the cube is 2 cm.
Find the value of x, such that f(x) is increasing function.
f(x) = 2x3 - 15x2 - 144x - 7
Find the value of x, such that f(x) is decreasing function.
f(x) = 2x3 – 15x2 – 84x – 7
Choose the correct alternative.
The function f(x) = x3 - 3x2 + 3x - 100, x ∈ R is
Let f(x) = x3 − 6x2 + 9𝑥 + 18, then f(x) is strictly decreasing in ______
The total cost function for production of articles is given as C = 100 + 600x – 3x2, then the values of x for which the total cost is decreasing 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:
Which of the following graph represent the strictly increasing function.
Let 'a' be a real number such that the function f(x) = ax2 + 6x – 15, x ∈ R is increasing in `(-∞, 3/4)` and decreasing in `(3/4, ∞)`. Then the function g(x) = ax2 – 6x + 15, x∈R has a ______.
