Unformatted text preview: 4. All inexpensive essays are boring. 5. ∀ x. ( x ∈ B ) → (( x ∈ H ) ∨ ( x / ∈ E )) 6. ∃ x. ( x ∈ H → x ∈ B ) ∧ ( x / ∈ E ) Problem 3 (5 points) Let O = { 2 k1  k ∈ Z } be the set of all odd integers. 1. Use set notation to deﬁne the set T of all integers that are the sum of two odd numbers 2. Use set notation to deﬁne the set S of all pairs of integers whose sum is odd 3. Use set notation to deﬁne the set P of all pairs of integers whose product is odd 4. Use set notation and the deﬁnition of T,S,P to formulate the statement “The product of any two odd integers is odd”. 5. Do the same for the statement “For any two numbers x and y , the sum x + y is odd if and only if the product x · y is odd.”...
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 Spring '08
 Foster
 Set Theory, Naive set theory, Natural number, historical essays

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