MGF 1106 Exam 1
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Collection or group of objects (ex: favorite color)
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Set
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Constant set (ex: multiples of 3)
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Well-defined set
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X is an element of A
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X?A
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X is not an element of A
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X?A
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{ }
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Roster method
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{x|x is a multiple of 3}
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Set builder notation
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A is a subset of B
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A?B
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2^x = # (x is number of elements, # is the number of subsets)
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Equation to find number of subsets
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2^x - 1
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Equation to find number or proper subsets
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What they share
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A?B
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Everything
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A?B
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A?B
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{x|x ? A and x?B}
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A?B
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{x|x ? A or x?B}
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A'
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{x|x ? A and x?B}
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U
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U??=?
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?
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U??=?
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Number of elements in A (cardinal number of A)
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n(A)
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n(A?B) = n(A) + n(B) - n(A?B)
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IMPORTANT FORMULA #1
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1
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How many components in a simple statement?
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More than 1
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How many components in a compound statement?
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conjunction: and, but
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?
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disjunction: or
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?
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not, it is not the case that
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~
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~p ? ~q
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~(p?q)
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~p ? ~q
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~(p?q)
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Some are not
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Negation of "all"
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Some are
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Negation of "never/none"
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9 + 8 = 16 9 + 8 ; 16
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List the components of the compound statement: 9 + 8 ? 16
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proper subset
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?
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subset
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?
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Any set is a subset of itself
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A?A
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A proper subset of A is any subset strictly smaller than A
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A?A
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The empty set is a subset (and proper subset) of any set A
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??A