Let A = { n ∈ Z ∣ n ≡ 1 ( mod 2 ), then A is the set of
Group of answer choices
even integers
odd integers
Z∖{0}
Z
None of the above
Q2
If A = { 1 } and B = { 2 }, then the power set, P ( A × B ) is
Group of answer choices
{ϕ,{A×B}}
{ϕ,{1×2}}
{ϕ,{(1,2)}}
{ϕ,{A}×{B}}
None of the above
Power of the (AxB) is
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Let R be the relation defined on Z (integers): a R b iff a + b is even. Then the distinct equivalence classes are: Group of answer choices [1] = multiples of 3 [2] = multiples of 4 [0] = even integers and [1] = the odd integers all the integers None of the above
Let R be the relation defined on Z (integers): a R b iff a + b is even. Suppose that 'even' is replaced by 'odd' . Which of the properties reflexive, symmetric and transitive does R possess? Group of answer choices Reflexive, Symmetric and Transitive Symmetric Symmetric and Reflexive Symmetric and Transitive None of the above
Define four sets of integers Let P {0, 1), let Q {-11, 1, 5) , and Let R and S be arbitrary nonempty subsets of Z. Define an even indicator function F F: ZP by F(x) = (x + 1) mod 2 for x e Z That is, F(x) 1 if x is even, and F(x) = 0 if x is odd. or neither? Explain. a) Is F: Q P one-to-one, onto, both, or neither? Explain. b) Is F: (Pn...
Consider the following recursive definition: if n=1 F(n)= | Fin - 1) +2 if n > 1 (O What set describes this definition? OOOO The set of nonnegative odd integers The set of even integers The set of nonnegative integers The set of odd integers none of the above The set of nonnegative even integers
ly(mod n). 2. Let n > 1 be an odd integer and suppose ? = y2 (mod n) for some x Prove that ged(x - yn) and ged(x + y, n) are nontrivial divisors of n.
Let R be the relation defined on Z (integers): a R b iff a + b is even. R is an equivalence relation since R is: Group of answer choices Reflexive, Symmetric and Transitive Symmetric and Reflexive or Transitive Reflexive or Transitive Symmetric and Transitive None of the above
27. (a) Let m and n be integers > 1 which are relatively prime. Show that the map f : Z → Z/mZ × Z/nZ whith f(x) = (x + mZ, x + nZ) is surjective (b) Prove the Chinese Remainder Theorem: If m and n are relatively prime integers > 1 and if a and b are any integers, then there exists a E Z such that b(mod n). a(mod m) and a a Hint: (a)] 27. (a) Let...
Let p be an odd prime. Prove that if g is a primitive root modulo p, then g^(p-1)/2 ≡ -1 (mod p). Let p be an odd prime. Prove that if g is a primitive root modulo p, then go-1)/2 =-1 (mod p) Hint: Use Lemma 2 from Chapter 28 (If p is prime and d(p 1), then cd-1 Ξ 0 (mod p) has exactly d solutions). Let p be an odd prime. Prove that if g is a primitive...
Please answer all!! 3. Show that if n e Z so that n is odd then 8|n2 + (n + 6)2 +6. 4. (a) Let a, b, and n be integers so that n > 2. Define: а is congruent to b mod n. The notation here is a = b (modn). (b) Is 12 = 4 (mod 2)? Explain. (c) Is 25 = 3 (mod 2)? Explain. (d) Is 27 = 13 (mod8)? Explain. (e) Find 6 integers x...
Need help!! Please help — crypto math 1. Determine L13(18) for p 19. 2. Let p be prime, and α a primitive root mod p. Prove that α(p-1)/2-_1 (mod p). 3. It can be shown that 5 is a primitive root for the prime 1223. You want to solve the discrete logarithm problem 53 (mod 1223). You know 3611 Prove it. 1 (mod 1223). Is x even or odd? 1. Determine L13(18) for p 19. 2. Let p be prime,...