22. Prove: if a, b, and c are odd, and a | b - c and a bc, then a | b and a c 22. Prove: if a, b, and c are odd, and a | b - c and a bc, then a | b and a c
22. Prove: if a, b, and c are odd, and a | b - c and a bc, then a | b and a c
13. Prove that for all integers b, if b is odd then b is odd
13. Prove that for all integers b, if b is odd then b is odd
Prove of disprove that if A, B and C are integers and the product BC is evenly divisible by A then either B is evenly divisible by A or C is evenly divisible by A.
Home work AB tAC t ABC A+BC Prove by truth table (AB)(A+B)C = A BC A+B ABC 2 Prove hy tra teble AAB+BAB + BA AB RB) ABc
How to prove this
3. [BC#1.5.8] Show that for any complex numbers zi,22 E C, we have = a1 +bi, etc.), or you can appeal to po- This can be done directly ( lar/exponential form(s)...
prove (h)
(e) A-B if and only if BC A. (f) An B Ø if and only if A C B De Morgan's Laws (h) (A B)c-Ac U Bc
Prove that if a and b are odd then 2gcd(a,b)=gcd(a+b,a−b)”
6. Prove that if a and b are odd integers, then a2 is divisible by 8. 7. Prove that if a is an odd integer, then ta + (a + 2)?+ (a +4)2 +1) is divisible by 12.
Prove that (for two events A and B) if A and Bc are independent, then A and B are independent
b. Prove that if a is an odd integer, then a | b2 – 1 implies that a = (a, b – 1)(a, b + 1).