Im just going through a practice exam and I was wondering If I could get someone to check my results.

Q1

a) [tex]X \backslash \{2\} = \{1,2,4,5\} \backslash \{2\} = \{1,4,5\}[/tex]

b) [tex]\{n \in X\,:\,n = 4\} = \{4\}[/tex]

c) [tex]\bigcap X = \bigcap \{1,2,4,5\} = 1 \cap 2 \cap 4 \cap 5 = \{0\}[/tex]

d) [tex]\bigcap \{X\} = X[/tex]

e) [tex]\bigcap\bigcap X = \bigcap \left( \bigcap \{1,2,4,5\}\right) = \bigcap (1 \cap 2 \cap 4 \cap 5) = \bigcap (\{\emptyset\}) = \emptyset[/tex]

f) [tex]\bigcup X = \bigcup \{1,2,4,5\} = 1 \cup 2 \cup 4 \cup 5 = 4[/tex]

g) [tex]\{n \in X\,:\, n \neq n\} = \{\emptyset\}[/tex]

h) [tex]X \cup \{0,1\} = \{1,2,4,5\} \cup \{0,1\} = X \cup \{0\}[/tex]

Q1

*Let [itex]X = \{1,2,4,5\}[/itex], where elements of [itex]X[/itex] are the sets [itex]1 = \{0\}[/itex], [itex]2 = 1 \cup \{1\}[/itex], etc. Evaluate each of the following:*a) [tex]X \backslash \{2\} = \{1,2,4,5\} \backslash \{2\} = \{1,4,5\}[/tex]

b) [tex]\{n \in X\,:\,n = 4\} = \{4\}[/tex]

c) [tex]\bigcap X = \bigcap \{1,2,4,5\} = 1 \cap 2 \cap 4 \cap 5 = \{0\}[/tex]

d) [tex]\bigcap \{X\} = X[/tex]

e) [tex]\bigcap\bigcap X = \bigcap \left( \bigcap \{1,2,4,5\}\right) = \bigcap (1 \cap 2 \cap 4 \cap 5) = \bigcap (\{\emptyset\}) = \emptyset[/tex]

f) [tex]\bigcup X = \bigcup \{1,2,4,5\} = 1 \cup 2 \cup 4 \cup 5 = 4[/tex]

g) [tex]\{n \in X\,:\, n \neq n\} = \{\emptyset\}[/tex]

h) [tex]X \cup \{0,1\} = \{1,2,4,5\} \cup \{0,1\} = X \cup \{0\}[/tex]

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