The solution set of the constraints |x-y| leq | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The given constraints are $|x-y| \leqslant 1$ and $x, y \geqslant 0$. The inequality $|x-y| \leqslant 1$ is equivalent to $-1 \leqslant x-y \leqsl

Vedclass · Accepted Answer

an unbounded set

Vedclass · Answer

(B) The given constraints are $|x-y| \leqslant 1$ and $x, y \geqslant 0$. The inequality $|x-y| \leqslant 1$ is equivalent to $-1 \leqslant x-y \leqslant 1$,which can be split into two inequalities: $y \leqslant x+1$ and $y \geqslant x-1$. Combining these with $x \geqslant 0$ and $y \geqslant 0$,we observe the region in the first quadrant. For any $x \geqslant 0$,we can choose $y$ such that $x-1 \leqslant y \leqslant x+1$. As $x$ increases indefinitely,$y$ can also increase indefinitely (e.g.,by choosing $y=x$). Since the region extends infinitely in the first quadrant,the solution set is an unbounded set.

The solution set of the constraints $|x-y| \leqslant 1, x, y \geqslant 0$ is

Similar Questions

The value of the greatest integer $k$ satisfying the inequation $2^{n+4} + 12 \geq k(n+4)$ for all $n \in \mathbb{N}$ is

The $I.Q.$ of a person is given by the formula $I.Q. = \frac{MA}{CA} \times 100$,where $MA$ is mental age and $CA$ is chronological age. If $75 < I.Q. < 125$ for a group of $16$ year old children,find the range of their mental age.

Solve $\frac{1 - |x|}{2 - |x|} \ge 0$.

Find the set of all values of $x$ satisfying $\frac{x^4 - 4x^3 + 3x^2}{(x^2 - 4)(x^2 - 7x + 10)} \ge 0$.

The region formed by the inequalities $2x + 3y - 5 \leq 0$,$4x - 3y + 2 \leq 0$,and $x \geq 0$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module