p q R s p → q r → s
T T T T T T F T T T F T F T T T F T T T F T T F F T T F T F T T F T T T F T F F F F T F F T F T T T F F F F T T F T T T T T F F T T F T F T F T F T T T F F T F F T T F F F T T T T F F F T F T
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( True ) At x = -1 ( (-1)2 + 2*-1 + 1 ≥ 0 ) ( 0 ≥ 0 )
. ( False ) At x = 1 , 0 , -1 , … ( (-1)2 + 2*-1 + 2 = 0 ) ( 1 ≠ 0 )
. ( False ) At x= -2 ( -2 > - (-2) ) ( -2 not > 2 )
. ( True ) At x = 0 ┐ ( 0 > 0 ) ┐ F = T
. ( True ) at x = -3 ( ( -3 )2 > 4 ) ^ ( -3 < 2 ) ( 9 > 4 ) ^ ( -3 < 2 )
Q¬−3: [2+3 marks] Find two finite sets A and B such that A ∈ B and A ⊂ B.
A = {2 ,4 ,┤ ├ 6} B = {1 ,2 ,4 ,├ 6 ,8 }┤
Give a proof of or a counterexample to the following statement:
A (B C) = (A B) (A C).
A = { 1 ,2 ,4 ,├ 7 }┤ B = { 2 ,5 ,7 ├ ,8}┤ C = {5 ,├ 9}┤ A (B
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( 2223 ) 4 8. ( 253 ) 8 16. ( AB )16 5. ( 1141 )5 7. ( 333 )7 a ) 3 4 171 2 4 42 2 4 10 2 4 2 0 b ) 3 8 171 5 8 21 2 8 2 0 c ) B 11 16 171 A 10 16 10 0 d ) 1 5 171 4 5 34 1 5 6 1 5 1 0 e ) 3 7 171 3 7 24 3 7 3 0 Q−5: [5 marks] Solve the following system of linear equations: (24 div 7) x + (25 mod 7) y = (-2 mod 13) (88 mod 6) x + (-10 div 6) y = (3 div 13) ( 24 = 7 * 3 + 3 ) x + ( 25 = 7 * 3 + 4 ) y = ( -2 = 13 * -1 + 11 ) 3X + 4y = 11 ( 88 = 14 *6 + 4 ) x + ( -10 = -2* 6 + 2 ) y = ( 3 = 13 *0 + 3 ) 4x – 2y = 0 3x + 4y = 11 4x – 2y = 0 (*2) 3x + 4y =