True or False. (1) Subset-of is a partial order defined on the set of all sets.

Question

True or False. (1) Subset-of is a partial order defined on the set of all sets.

(2) Subset-of is a total order defined on the set of all sets.

(3) Proper-subset-of is a partial order defined on the set of all sets.

(4) Proper-subset-of is a total order defined on the set of all sets.

(5) Less than or equal (<=) is a partial order defined on the set of real numbers.

(6) Less than or equal (<=) is a total order defined on the set of real numbers.

(7) Less than (<) is a partial order defined on the set of real numbers.

(8) Less than (<) is a total order defined on the set of real numbers.

Explanation / Answer

(1) Subset-of is a partial order defined on the set of all sets. TRUE

(2) Subset-of is a total order defined on the set of all sets. FALSE

(3) Proper-subset-of is a partial order defined on the set of all sets. TRUE

(4) Proper-subset-of is a total order defined on the set of all sets. FALSE

(5) Less than or equal (<=) is a partial order defined on the set of real numbers. TRUE

(6) Less than or equal (<=) is a total order defined on the set of real numbers. FALSE

(7) Less than (<) is a partial order defined on the set of real numbers. FALSE

(8) Less than (<) is a total order defined on the set of real numbers. TRUE

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