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# h2 - [10 Determine whether the following function is...

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[50] Homework 2. Language of Mathematics Each problem is worth 10 points [10] Prove that for any sets A and B A = ( A B ) ( A B ) . [10] Let x and y be integers . Determine whether the following relations are reflexive, sym- metric, antisymmetric, or transitive: x y mod 7; xy 1; x = y 2 . Justify your statements. Finally, determine which of the above relations are equivalence and partial order relations. For equivalence relations, construct the equivalence classes.
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Unformatted text preview: [10] Determine whether the following function is bijection from R to f ( R ): • f ( x ) = x 3 • f ( x ) = sin 2 ( x ) • f ( x ) = x +1 x +2 . [10] Let g ( x ) = ⌊ x ⌋ . ±ind • g-1 ( { } ); • g-1 ( { x : 0 < x < 1 } ) [10] What are the values of the following: 500 s i =1 5 i , 2 s i =1 3 s j =1 ( i + j ) 8 s j =0 (3 j − 2 j ) . 1...
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