# HW1 - A B (NOT A ) OR (NOT B ) True True True False False...

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Name: Math 100 Due Friday, October 5, 2:00 pm Homework 1 1. (1 point) Write a purely symbolic sentence, which incorporates boolean conjunctions, at least three diﬀerent operations, and two diﬀerent relations. 2. (1 point) Is the following sentence true or false: ((2 + 3 = 5) AND (1 + 3 = 5)) OR (NOT (6 × 10 = 59)). 3. (2 points) Fill in the missing boxes in the following two truth tables. What can you conclude? (a) The truth table for “NOT (A AND B)” A B NOT ( A AND B ) True True True False False True False False (b) The truth table for “(NOT A) OR (NOT B)”

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Unformatted text preview: A B (NOT A ) OR (NOT B ) True True True False False True False False 4. (1 point) Write a purely symbolic sentence involving two variables and both quantiﬁers. 5. (2 points) Are the following sentences true or false? (a) ∀ x ∈ R ,x 2 > x. (b) ∃ y ∈ R , ∀ x ∈ R , ( x 2 + y ) > x. 6. (1 point) Express the following English sentence symbolically: Whenever two real numbers are distinct, one can ﬁnd a real number between them. Page 2...
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## This homework help was uploaded on 04/17/2008 for the course MATH 100 taught by Professor Weissman during the Fall '08 term at UCSC.

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HW1 - A B (NOT A ) OR (NOT B ) True True True False False...

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