Decide whether each of the following statements are true. (a) Ifa,b,m,n∈N and a|m and b|n,then ab|mn. (b) If a,b,m,n∈N and ab|mn,the neither a|m or b|n. [Justify your answers.

Q: 17. Evaluate V|r|3 A. rr В. 2rr C. 4rr D. 3rr

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Q: 4. Let B = {1, 2, 3, 4, 3, 2, 1}. What is |B|?

A: We will solve the following

Q: Let A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} and C = {a, b, c, d}. What is |A × C|?

A: Given that A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} and C = {a, b, c, d}.  We have to find |A × C|.

Q: 6. Let A= {1,3,5), B = {2,4,6,8), C={2,3,4,5) Which of the following statements is false? A. An B=0…

A: We have to check which of the following statements is false.

Q: Let A = {1,2,3,..., 10}, B = {2,3,6,8), and C= {3, 5, 4, 8, 2}. Find the following:

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Q: and pigs in a field totals 35. The as exactly two legs and each pig h pigs are in the field. (Do not…

A: Given: Four playing boys marbles and their names have given.

Q: Answer whether it is true or false. a. Is 1 ∈ {1}? b. Is {2} ⊆ {1,{2},{3}}? c. Is {1} ⊆ {1, 2}? d.…

A: # we are entitled to solve three subparts, please resubmit the question with other sub parts if you…

Q: 1. P 2. P→Q 3. ¬QVR :.R 4. Q 5. Q 6. R 2,1 4 3,4

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Q: U = {1, 2, {1}, {2}, {1, 2}}      A = {1, 2, {1}}       B = {{1}, {1, 2}}       C = {2, {1}, {2}}.…

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Q: Y={a,b,c,d,f} Is the following statement True? ∅⊆Y

A: The given set is                        Y={ a , b , c , d , f } We know that for every set S , S⊂S ,…

Q: Which of the following are true statements? State why. d. {2} ⊆ {1,2,3} e. {2} ⊆ {{1},{2}} f. {2} ∈…

A: Statements:                       d) {2}⊆{1, 2, 3}                       e) {2}⊆{1, 2}f) {2}∈{1, 2}

Q: Let A, B, C, D be sets. (ANB)x(CND)=(AXC)n(BxD). True. False.

A: Use the basic properties of intersection and cartesian product to prove the given relation.

Q: elect values for a,b,c and d to create a counter-example that shows the following statement is…

A:

Q: H = {n: n is a positive even integer from 1 to 50} K = {n: n is a prime number from 1 to 50} J = {n:…

A:

Q: If a = (2, 4, – 1, 3) then ||-3a|l,= Select one: а. 30 b. -30 c. 27 d. -27

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Q: If |A|  8 and |B|  5, what is |A ∪ B| + |A ∩ B| ?

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Q: Let A = {0, 2, 4, 6}, B = {1, 2, 3, 4, 5}, and C = {1, 3, 5, 7}. Find A n C. ||

A: Given, A = {0,2,4,6} B = {1,2,3,4,5} C = {1,3,5,7}

Q: If a|b, then a|(bc). Direct proof.

A:

Q: I. TRUE OR FALSE. Write 1 if the statement is always true. Otherwise write 0. 8. For any sets A, B,…

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Q: Let R = {(a, b), (b, a), (a, c), (c, d), (d, a)} a. Is (a, c) E R³? b. Is (a, a) E R²? c. Is (c, c)…

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Q: a|b → a is multiple of b.

A: a|b means a divides b. So b = na

Q: Let ā = (5, 1, −1) and ỗ = (2, 1, 4). Find a. b.

A:

Q: If |A| = 9 and |B| = 7, what is |A U B|+|An B|?

A: =9 ,=7 to find |+

Q: Let U= {q, r, s, t, u, v, w, x, y, z}; A = {q, s, u, w, y}; B = {q, s, y, z} and C = {v, w, x, y,…

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Q: (a) A child has a box of candy which might have a toy inside. The probability of the box having a…

A: given data , here we have to find out the probability of the events formula of odds against event…