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Prove S1 without using venn -diagram ( using boolean algebra )

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$A\cup \left ( B-C \right )$

$A\cup \left ( B\cap \bar{C} \right )$

$\left ( A\cup B \right )\cap \left ( A\cup \bar{C} \right )$

$\left ( A\cup B \right )-(\overline{A\cup \bar{C}})$

$(A\cup B)-(\bar{A}\cap C)$

$(A\cup B)-((1-A)\cap C)$

$(A\cup B)-((1-A)- \bar{C})$

$(A\cup B)-((1-A)-(1-C))$

$(A\cup B)-(C-A)$
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