Let Qx, y) be the predicate "If x < y then x < y- with domain for both x and y being R, the set of all real numbers. (a) When x-2 and y 1, is QIX, v) true or false? The hypothesis of Q(-2, 1) is -2 <1 v , which is true The conclusion is 4<1 which is false Thus Q(-2, 1) is a conditional statement with a true v hypothesis and a false v conclusion. So Q(-2, 1) is false (b) Give values different from those in part (a) for which Q(x, y) has the same truth value as in part (a). (x. V) = (L (c) When x = 3 and y = 8, is Q(x, y) true or false? The hypothesis of Q(3, 8) is (3<8 vwhich is true The conclusion is 9<64 which is true Thus Q(3, 8) is a conditional statement with a true Vv hypothesis and a true Vv conclusion. So Q(3, 8) is true (4) Give values different from those in part (e) for which Q(x, y) has the same truth values as in part (c).

Advanced Engineering Mathematics
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ISBN:9780470458365
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Chapter2: Second-order Linear Odes
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Let Q(x, y) be the predicate "If x < y then x? < y?," with domain for both x and y being R, the set of all real numbers.
(a) When x = -2 and y = 1, is Q(x, y) true or false?
The hypothesis of Q(-2, 1) is -2 < 1
, which is true
. The conclusion is 4 < 1
which is false
. Thus Q(-2, 1) is a conditional statement with a true
V hypothesis and a false
conclusion. So Q(-2, 1) is false
(b) Give values different from those in part (a) for which Q(x, y) has the same truth value as in part (a).
(х, у) %3D
(c) When x = 3 and y = 8, is Q(x, y) true or false?
The hypothesis of Q(3, 8) is 3 < 8
, which is true
The conclusion is 9 < 64
, which is true
Thus Q(3, 8) is a conditional statement with a true
V hypothesis and a true
vy conclusion. So Q(3, 8) is true
(d) Give values different from those in part (c) for which Q(x, y) has the same truth values as in part (c).
(х, у) %3D
Transcribed Image Text:Let Q(x, y) be the predicate "If x < y then x? < y?," with domain for both x and y being R, the set of all real numbers. (a) When x = -2 and y = 1, is Q(x, y) true or false? The hypothesis of Q(-2, 1) is -2 < 1 , which is true . The conclusion is 4 < 1 which is false . Thus Q(-2, 1) is a conditional statement with a true V hypothesis and a false conclusion. So Q(-2, 1) is false (b) Give values different from those in part (a) for which Q(x, y) has the same truth value as in part (a). (х, у) %3D (c) When x = 3 and y = 8, is Q(x, y) true or false? The hypothesis of Q(3, 8) is 3 < 8 , which is true The conclusion is 9 < 64 , which is true Thus Q(3, 8) is a conditional statement with a true V hypothesis and a true vy conclusion. So Q(3, 8) is true (d) Give values different from those in part (c) for which Q(x, y) has the same truth values as in part (c). (х, у) %3D
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