Consider the following statement. If x is nonnegative, then x is positive or x is 0. In (a)-(d) below, select the negation, contrapositive, converse, and inverse for the statement. (Assume that all variables represent fixed quantities or entities, as appropriate.) (a) Negation O fxis not positive and x is not 0, then x is not nonnegative. O fx is positive or x is 0, then x is nonnegative. O fxis not nonnegative, then both x is not positive and x is not 0. O fxis not nonnegative, then x is positive or x is 0. O xis nonnegative and x is not positive and x is not 0. (b) Contrapositive O fxis not positive and x is not 0, then x is not nonnegative. O ffx is positive or x is 0, then x is nonnegative. O fxis not nonnegative, then both x is not positive and x is not 0. O fxis not nonnegative, then x is positive or x is 0. O xis nonnegative and x is not positive and x is not 0. (c) Converse O fxis not positive and x is not 0, then x is not nonnegative. O fxis positive or x is 0, then x is nonnegative. O fxis not nonnegative, then both x is not positive and x is not 0. O fxis not nonnegative, then x is positive or x is 0. O xis nonnegative and x is not positive and x is (d) Inverse O fxis not positive and x is not 0, then x is not nonnegative. O fx is positive or x is 0, then x is nonnegative. O fxis not nonnegative, then both x is not positive and x is not 0. O fx is not nonnegative, then x is positive or x is 0. O xis nonnegative and x is not positive and x is not 0.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Consider the following statement.
If x is nonnegative, then x is positive or x is 0.
In (a)-(d) below, select the negation, contrapositive, converse, and inverse for the statement. (Assume that all variables represent fixed quantities or entities, as appropriate.)
(a) Negation
O fxis not positive and x is not 0, then x is not nonnegative.
O fx is positive or x is 0, then x is nonnegative.
O fxis not nonnegative, then both x is not positive and x is not 0.
O fxis not nonnegative, then x is positive or x is 0.
O xis nonnegative and x is not positive and x is not 0.
(b) Contrapositive
O fxis not positive and x is not 0, then x is not nonnegative.
O ffx is positive or x is 0, then x is nonnegative.
O fxis not nonnegative, then both x is not positive and x is not 0.
O fxis not nonnegative, then x is positive or x is 0.
O xis nonnegative and x is not positive and x is not 0.
(c) Converse
O fxis not positive and x is not 0, then x is not nonnegative.
O fxis positive or x is 0, then x is nonnegative.
O fxis not nonnegative, then both x is not positive and x is not 0.
O fxis not nonnegative, then x is positive or x is 0.
O xis nonnegative and x is not positive and x is
(d) Inverse
O fxis not positive and x is not 0, then x is not nonnegative.
O fx is positive or x is 0, then x is nonnegative.
O fxis not nonnegative, then both x is not positive and x is not 0.
O fx is not nonnegative, then x is positive or x is 0.
O xis nonnegative and x is not positive and x is not 0.
Transcribed Image Text:Consider the following statement. If x is nonnegative, then x is positive or x is 0. In (a)-(d) below, select the negation, contrapositive, converse, and inverse for the statement. (Assume that all variables represent fixed quantities or entities, as appropriate.) (a) Negation O fxis not positive and x is not 0, then x is not nonnegative. O fx is positive or x is 0, then x is nonnegative. O fxis not nonnegative, then both x is not positive and x is not 0. O fxis not nonnegative, then x is positive or x is 0. O xis nonnegative and x is not positive and x is not 0. (b) Contrapositive O fxis not positive and x is not 0, then x is not nonnegative. O ffx is positive or x is 0, then x is nonnegative. O fxis not nonnegative, then both x is not positive and x is not 0. O fxis not nonnegative, then x is positive or x is 0. O xis nonnegative and x is not positive and x is not 0. (c) Converse O fxis not positive and x is not 0, then x is not nonnegative. O fxis positive or x is 0, then x is nonnegative. O fxis not nonnegative, then both x is not positive and x is not 0. O fxis not nonnegative, then x is positive or x is 0. O xis nonnegative and x is not positive and x is (d) Inverse O fxis not positive and x is not 0, then x is not nonnegative. O fx is positive or x is 0, then x is nonnegative. O fxis not nonnegative, then both x is not positive and x is not 0. O fx is not nonnegative, then x is positive or x is 0. O xis nonnegative and x is not positive and x is not 0.
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