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I. TRUE OR FALSE. Write 1 if the statement is always true. Otherwise write 0. 1. The converse of statement Q P is logically equivalent to -Q ¬P.

I. TRUE OR FALSE. Write 1 if the statement is always true. Otherwise write 0. 1. The converse of statement Q P is logically equivalent to -Q ¬P.

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.3: Divisibility
Problem 10TFE
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I. TRUE OR FALSE. Write 1 if the statement is always true. Otherwise write 0. 1. The converse of statement Q P is logically equivalent to -Q ¬P. 2. The negation of the statement "For every e > 0 there exists a d > 0 such that if 0 < |x – a| < 8 then |f(x) – L < e " is the statement " There exists an e > 0 such that for all & > 0, we have 0< |x – al < ô and |f(x) – L| > e. " 3. The statement SA (T S) = T is a contradiction. For item 4, suppose the following statements are true: Blosem, Babels, and Batakab all took a ComSci 55 exam. Either Batakab or Babels or both got a perfect score. If Batakab's score is below 100% then Babels's score is also below 100%. If Batakab got a perfect score then so is Blosem. Either Blosem or Babels got a perfect score but not both. 4. Batakab got a perfect score in their exam. 5. Consider the false statement Vr, y E Q, x < y = !> !. A counterexample is x = -1 and y = -2. 6. For all positive real numbers x and y, if x2 + xy+ y? < 0 then x < 0. 7. For any sets A, B, D, if B C A then D- A CD- B. 8. For any sets A, B, we have A – B = (B – A)'. 9. Let I = {A1, A2, A3} where A_i={1, i-1, i+1} for all i = 1, 2, 3. Then |UT = 6. 10. Ø C {0}.
Transcribed Image Text:I. TRUE OR FALSE. Write 1 if the statement is always true. Otherwise write 0. 1. The converse of statement Q P is logically equivalent to -Q ¬P. 2. The negation of the statement "For every e > 0 there exists a d > 0 such that if 0 < |x – a| < 8 then |f(x) – L < e " is the statement " There exists an e > 0 such that for all & > 0, we have 0< |x – al < ô and |f(x) – L| > e. " 3. The statement SA (T S) = T is a contradiction. For item 4, suppose the following statements are true: Blosem, Babels, and Batakab all took a ComSci 55 exam. Either Batakab or Babels or both got a perfect score. If Batakab's score is below 100% then Babels's score is also below 100%. If Batakab got a perfect score then so is Blosem. Either Blosem or Babels got a perfect score but not both. 4. Batakab got a perfect score in their exam. 5. Consider the false statement Vr, y E Q, x < y = !> !. A counterexample is x = -1 and y = -2. 6. For all positive real numbers x and y, if x2 + xy+ y? < 0 then x < 0. 7. For any sets A, B, D, if B C A then D- A CD- B. 8. For any sets A, B, we have A – B = (B – A)'. 9. Let I = {A1, A2, A3} where A_i={1, i-1, i+1} for all i = 1, 2, 3. Then |UT = 6. 10. Ø C {0}.
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