Question

Please help me on 22 and 28 please. Thank you

Answer 1

`\sf 22. \quad \left(Y \cap X'\right) \cup Z = \{b,c,d,e,f\}`

`\sf 28. \quad Y\;\!'-X = \{d, f\}`

Explanation:

Set notation

`\begin{array}c \cline{1-3} \sf Symbol & \sf N\:\!ame & \sf Meaning \\\cline{1-3} \{ \: \} & \sf Set & \sf A\:collection\:of\:elements\\\cline{1-3} \cup & \sf Union & \sf A \cup B=elements\:in\:A\:or\:B\:(or\:both)}\\\cline{1-3} \cap & \sf Intersection & \sf A \cap B=elements\: in \:both\: A \:and \:B} \\\cline{1-3} \sf ' \:or\: ^c & \sf Complement & \sf A'=elements\: not\: in\: A \\\cline{1-3} \sf - & \sf Difference & \sf A-B=elements \:in \:A \:but\: not\: in \:B}\\\cline{1-3} \end{array}`

Given sets:

• X = {a, c, e, g}
• Y = {a, b, c}
• Z = {b, c, d, e, f}

Therefore,

• Universal set = {a, b, c, d, e, f, g}
• X' = not in X = {b, d, f}
• Y' = not in Y = {d, e, f, g}

Question 22

`\begin{aligned}\sf \left(Y \cap X'\right) \cup Z & = \sf \left(\{a,b,c\} \cap \{b,d,f\}\right) \cup \{ b,c,d,e,f \}\\& = \sf \{b\} \cup \{b,c,d,e,f\}\\& = \sf \{b,c,d,e,f\}\end{aligned}`

Question 28

`\begin{aligned}\sf Y'-X & = \sf \{d,e,f,g\} - \{a,c,e,g\}\\& = \sf \{d,f\}\end{aligned}`