Unformatted text preview: A;B;C we have ( A ² B ) \ ( A ² C ) \ ( B [ C ) = ± . 8. Show by induction that 4 n + 24 n ² 10 is divisible by 18 for every n 2 N . 9. Let P ( x ) be assertion \ x is prime", E ( x ) be \ x is even", and D ( x;y ) be \ x divides y " (i.e., y x is an integer). Consider the following statement: R = ( 8 x 2 Z )( P ( x ) ) (( 9 y 2 Z )( E ( y ) ^ D ( x;y )))) Write the negation of R , and determine which statement is true, R or : R . 10. Show that for every n 2 N , 3 4 n +2 + 1 is divisible by 10 . 11. If P and Q are two statements, ±nd among the following statements, the negation of P , Q , and one which is equivalent to P , Q . Justify your answer: ( : P ) , Q ; ( : P ) , ( : Q ) ; ( P ) Q ) _ ( Q ) P ) ; P ^ Q 12. Prove that for any three sets A;B;C : A ² ( B ² C ) = ( A ² B ) [ ( A \ C ) ....
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 Spring '10
 Math

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