# 1) Given sets A and B as A= (0, 1, 2), and B=(a,b), (i) Write...

 

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# 1) Given sets A and B as A= (0, 1, 2), and B=(a,b), (i) Write all the elements of powerset 2A (ii) Write all the elements of the Cartesian product A x B. #2) Prove by induction: For all! Integers n 21, the integer 5"-1 is divisible by 4. # 3) Prove by counter example: If a sum of two integers is even, then one of the summands is even. # 4) Prove by contradiction: if 3n+ 2 is an odd integer, then n is odd (Hint: odd integer is represented as 2k+1 where k is an integer) # 1) Given sets A and B as A= (0, 1, 2), and B=(a,b), (i) Write all the elements of powerset 2A (ii) Write all the elements of the Cartesian product A x B. #2) Prove by induction: For all! Integers n 21, the integer 5"-1 is divisible by 4. # 3) Prove by counter example: If a sum of two integers is even, then one of the summands is even. # 4) Prove by contradiction: if 3n+ 2 is an odd integer, then n is odd (Hint: odd integer is represented as 2k+1 where k is an integer)

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1i Powerset of 2A 012010212012 ii Cartesian product of A x B 0a0b1a1b2a2b 2 Proof by induction The s... View the full answer