Zbiory

[agaaw1]

\(A={x \in R:(1-0.5x)^2>3-(2-0,5x)(0,5x+2}\)
\(B=x \in R:-3x \le 12\)
\(C= \left\langle 0;6\right\rangle\)
A \cup B
A \cap B'
(A \cup C)\B

[eresh]

\(A={x \in R:(1-0.5x)^2>3-(2-0,5x)(0,5x+2}\)
\(B=x \in R:-3x \le 12\)
\(C= \left\langle 0;6\right\rangle\)
A \cup B
A \cap B'
(A \cup C)\B

\((1-0,5x)^2>3-(2-0,5x)(0,5x+2)\\
1-x+0,25x^2>3-(4-0,25x^2)\\
1-x+0,25x^2>3-4+0,25x^2\\
-x>-2\\
x<2\\
A=(-\infty, 2)
\)

\(-3x\leq 12\\
x\geq -4\\
B=[-4,\infty)\)

\(A\cup B=\mathbb{R}\\
A\cap B'=(-\infty, -4)\\
(A\cup C)\setminus B=(-\infty, 6]\setminus B=(-\infty. -4)\)