Advertisements
Advertisements
प्रश्न
Using truth table show that ∼ (p → ∼ q) ≡ p ∧ q
Advertisements
उत्तर
∼ (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
संबंधित प्रश्न
Show that the function `f(x) = x^3 - 3x^2 + 6x - 100` is increasing on R
Prove that the function f given by f(x) = x2 − x + 1 is neither strictly increasing nor strictly decreasing on (−1, 1).
On which of the following intervals is the function f given byf(x) = x100 + sin x –1 strictly decreasing?
Show that f(x) = \[\frac{1}{x}\] is a decreasing function on (0, ∞) ?
Find the interval in which the following function are increasing or decreasing f(x) = x3 − 12x2 + 36x + 17 ?
Show that f(x) = x − sin x is increasing for all x ∈ R ?
Show that f(x) = x3 − 15x2 + 75x − 50 is an increasing function for all x ∈ R ?
Determine whether f(x) = −x/2 + sin x is increasing or decreasing on (−π/3, π/3) ?
If the function f(x) = 2x2 − kx + 5 is increasing on [1, 2], then k lies in the interval
The function f(x) = x2 e−x is monotonic increasing when
Test whether the following functions are increasing or decreasing : f(x) = 2 – 3x + 3x2 – x3, x ∈ R.
Find the values of x for which the function f(x) = x3 – 12x2 – 144x + 13 (a) increasing (b) decreasing
Find the values of x for which the function f(x) = x3 – 6x2 – 36x + 7 is strictly increasing
If the function f(x) = `7/x - 3`, x ∈ R, x ≠ 0 is a decreasing function, then x ∈ ______
The function f(x) = `(2x^2 - 1)/x^4`, x > 0, decreases in the interval ______.
The function f (x) = x2, for all real x, is ____________.
If f(x) = `x - 1/x`, x∈R, x ≠ 0 then f(x) is increasing.
If f(x) = `x/(x^2 + 1)` is increasing function then the value of x lies in ______.
If \[f'(x)<0\] throughout an interval, then \[f\] is
