Consider the following statement that refers to the Tarski world introduced in Example 3.3.1 and shown again below. v cirde x and v triangle y, x is above y. b d' j (a) Which of the following is a negation for the statement? O 3 a circle x and 3 a triangle y such that x is not above y. O a triangle y such that v cirde x, y is above x. O v rde x and v triangle y, y is below x. O v irde x and v triangle y, x is not above y. O 3 a circde x and 3 a triangle y such that y is belovw x. (b) Is the given statement true or false? Choose values of x and y that will elp answer this question, and enter them here. (x, y) = When you substitute the values you filled in for x and y, which of the choices below answers the question? O The statement is true. Proof: Let x and y be the figures in the ordered pair above. Then x is a circle and y is a triangle and x is above y. O The statement is true. Proof: Let x and y be the figures in the ordered pair above. Then x is a circle and y is a triangle and x is above both y and every other triangle in the Tarski worle O The statement is false. Counterexample: Let x and y be the figures in the ordered pair above. Then x is a circle and y is a triangle but x is not above y. O The statement is false. Counterexample: Let x and y be the figures in the ordered pair above. Then x is a circle and y is a triangle but x is lower than y.
Consider the following statement that refers to the Tarski world introduced in Example 3.3.1 and shown again below. v cirde x and v triangle y, x is above y. b d' j (a) Which of the following is a negation for the statement? O 3 a circle x and 3 a triangle y such that x is not above y. O a triangle y such that v cirde x, y is above x. O v rde x and v triangle y, y is below x. O v irde x and v triangle y, x is not above y. O 3 a circde x and 3 a triangle y such that y is belovw x. (b) Is the given statement true or false? Choose values of x and y that will elp answer this question, and enter them here. (x, y) = When you substitute the values you filled in for x and y, which of the choices below answers the question? O The statement is true. Proof: Let x and y be the figures in the ordered pair above. Then x is a circle and y is a triangle and x is above y. O The statement is true. Proof: Let x and y be the figures in the ordered pair above. Then x is a circle and y is a triangle and x is above both y and every other triangle in the Tarski worle O The statement is false. Counterexample: Let x and y be the figures in the ordered pair above. Then x is a circle and y is a triangle but x is not above y. O The statement is false. Counterexample: Let x and y be the figures in the ordered pair above. Then x is a circle and y is a triangle but x is lower than y.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter5: Rings, Integral Domains, And Fields
Section5.3: The Field Of Quotients Of An Integral Domain
Problem 6E
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Transcribed Image Text:Consider the following statement that refers to the Tarski world introduced in Example 3.3.1 and shown again below.
v cirde x and v triangle y, x is above y.
b
d'
j
(a) Which of the following is a negation for the statement?
O 3 a circle x and 3 a triangle y such that x is not above y.
O a triangle y such that v cirde x, y is above x.
O v rde x and v triangle y, y is below x.
O v irde x and v triangle y, x is not above y.
O 3 a circde x and 3 a triangle y such that y is belovw x.
(b) Is the given statement true or false? Choose values of x and y that will elp answer this question, and enter them here.
(x, y) =
When you substitute the values you filled in for x and y, which of the choices below answers the question?
O The statement is true. Proof: Let x and y be the figures in the ordered pair above. Then x is a circle and y is a triangle and x is above y.
O The statement is true. Proof: Let x and y be the figures in the ordered pair above. Then x is a circle and y is a triangle and x is above both y and every other triangle in the Tarski worle
O The statement is false. Counterexample: Let x and y be the figures in the ordered pair above. Then x is a circle and y is a triangle but x is not above y.
O The statement is false. Counterexample: Let x and y be the figures in the ordered pair above. Then x is a circle and y is a triangle but x is lower than y.
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