Hello! I'm really having a hard time in set theoretic proofs. Please help me with these two items. Thanks! Let U be a universal set and A, B, C C U.ITEM 1. Prove: A n B C A U BITEM 2. Prove: (A U B)C = AC n BC

# as per the guidelines we are entitled to solve one question at a time please resubmit the other…

Answered: Let U be a universal set and A, B, C…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Suppose we want to choose 6 objects, without replacement, from 9 distinct objects. (If necessary, consult a list of formulas.) (a) How many ways can this be done, if the order of the choices matters? ☐ (b) How many ways can this be done, if the order of the choices does not matter? ☐
Suppose we want to choose 6 objects, without replacement, from 10 distinct objects. (If necessary, consult a list of formulas.) (a) How many ways can this be done, if the order of the choices does not matter? ☐ (b) How many ways can this be done, if the order of the choices matters?
please answer with proper explanation and step by step solution.
Question 4. The following are logical laws shown in our lecture. Find their dual versions if exist. Implication law Idempotent law Соmmutative law A → B = ¬AV B AA A = A АЛВ 3D ВЛА (АЛ В) ЛС 3D Ал (ВЛС) Ал (AV B) А A A (B V C) Associative law Absorption law = (A ^ B) V (A ^ C) Distributive law Double Negation law De Morgan's law Excluded middle law A ¬(A ^ B) = ¬A V¬B AA¬A = F АЛТ 3D А Identity law Domination law AAF = F
is the following true / false / maybe ? " in transportation problem , the number of basic ( primal) variables is equal to the number of dual variables."
Please use justification for each step.
The following is a list of converse statement of modular arithmetic. Determine if any of the following results hold true. ACTIVITIES AND ASSIGNMENTS FOR WEEK 2 3 (0) If a x k = b x k mod n for any integer k, then (r) If a = b' mod n for any positive integer l, then a = b mod n. (p) If a² = b² mod n, then a = b mod n. (g) If a³ = b³ mod n, then a = b mod n. a = b mod n. (s) If 2ª = 2º mod n, then a = b mod n. (t) If 3ª = 3º mod n, then a = b mod n. 3 Again, remember that the above list from (a) to (t) are not all true. Some of them are false. Pick your favorite fact and do the followings:
Thank you so much, could you perhaps elaborate the proofs a bit more, I understand it but somehow it doesnt make sense for me, if perhaps you could use the definitions to elaborate more i would be grateful.
Show by concrete examples that the de Morgan’s Law and its duality is true.

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Let U be a universal set and A, B, C CU. ITEM 1. Prove: A n BCAUB