Question

VA ROGG AJUTAȚI DAU COROANA ȘI CÂT MAI REPEDE TEROGGGG​

Answer 1

$\dfrac{5}{2}x + 1 = \dfrac{3}{2}$

$5x + 2 = 3 \iff 5x = 1 \implies x = \dfrac{1}{5}$

$\implies A = \bigg\{\dfrac{1}{5}\bigg\}$

$a \in \{1;3;5;7;9;11;13;15\}$

$\dfrac{5}{5} = 1; \dfrac{15}{5} = 3$

$\implies B = \bigg\{\dfrac{1}{5}; \dfrac{3}{5}; 1; \dfrac{7}{5}; \dfrac{9}{5}; \dfrac{11}{5}; \dfrac{13}{5}; 3\bigg\}$

$n \in \{0;1;2;3\}$

$n = 0 \iff \dfrac{2^{0+1}}{5^{0}} = \dfrac{2}{1} = 2$

$n = 1 \iff \dfrac{2^{1+1}}{5^{1}} = \dfrac{2^{2}}{5} = \dfrac{4}{5}$

$n = 2 \iff \dfrac{2^{2+1}}{5^{2}} = \dfrac{2^{3}}{25} = \dfrac{8}{25}$

$n = 3 \iff \dfrac{2^{3+1}}{5^{3}} = \dfrac{2^{4}}{125} = \dfrac{16}{125}$

$\implies C = \bigg\{\dfrac{16}{125}; \dfrac{8}{25}; \dfrac{4}{5}; 2\bigg\}$

=>

$A \cap B = \bigg\{\dfrac{1}{5}\bigg\}\iff A \cap B = A$

$A \cup C = \bigg\{\dfrac{16}{125}; \dfrac{8}{25}; \dfrac{1}{5};\dfrac{4}{5}; 2\bigg\}$

$card \ C = 4$

$A \cup B = \bigg\{\dfrac{1}{5}; \dfrac{3}{5}; 1; \dfrac{7}{5}; \dfrac{9}{5}; \dfrac{11}{5}; \dfrac{13}{5}; 3\bigg\}$

$\iff A \cup B = B$

$B \cup C = \bigg\{\dfrac{16}{125}; \dfrac{8}{25}; \dfrac{1}{5}; \dfrac{3}{5}; \dfrac{4}{5}; 1; \dfrac{7}{5}; \dfrac{9}{5};2; \dfrac{11}{5}; \dfrac{13}{5}; 3\bigg\}$

$B \cap C = \O \implies card (B \cap C) = 0$