Chapter 2 Probability - 2.2 Sample Spaces and the Algebra of Sets - Questions - Page 25: 36

a)The event \[{{(A\cap {{B}^{C}})}^{C}}\] is equivalent to \[({{A}^{C}}\cup B)\text{ or }{{A}^{C}}\cup (A\cap B)\] b)The event \[B\cup {{(A\cup B)}^{C}}\] is equivalent to \[{{(A\cap {{B}^{C}})}^{C}}\text{ or }{{A}^{C}}\cup (A\cap B)\] c)The event \[A\cup {{(A\cap B)}^{C}}\] is equivalent to \[(A\cap {{B}^{C}})\text{ or }{{B}^{C}}\cap (A\cup B)\]

a)The event \[{{(A\cap {{B}^{C}})}^{C}}\] is equivalent to \[({{A}^{C}}\cup B)\text{ or }{{A}^{C}}\cup (A\cap B)\] b)The event \[B\cup {{(A\cup B)}^{C}}\] is equivalent to \[{{(A\cap {{B}^{C}})}^{C}}\text{ or }{{A}^{C}}\cup (A\cap B)\] c)The event \[A\cup {{(A\cap B)}^{C}}\] is equivalent to \[(A\cap {{B}^{C}})\text{ or }{{B}^{C}}\cap (A\cup B)\]