. Use the Set Identities to verify the following, and indicatewhichlawisused for eachstep of the ...
Use sum and difference identities to verify which of the following are identities. 1) sin(Q+8) - 1-tan & tan 8 sin a 2-cot a cot 8 2) cos(a+8) - 2 sin a sin 8 Both the equations are identities. None of the equations are identities Only the first equation is an identity. Only the second equation is an identity.
3. (12') Using Venn diagrams, verify the following identities. (a) A-(AnB)U(A-B) ( b) If A and B are finite sets, we have (AUB)- A+B-(AnB )
Use membership tables (i.e., no set identities or Venn diagrams) to demonstrate that 4. Use membership tables (i.e., no set identities or Venn diagrams) to demonstrate that ((Y U Z) n (X UZ)) – (Y nz) and (2 U(Y nx)) ((CY NZ) ux)u((YnZ)n x)) are equivalent expressions. (5 marks)
6. Let A, B, and C be subsets of some universal set U. Prove or disprove each of the following: * (a) (A n B)-C = (A-C) n (B-C) (b) (AUB)-(A nB)=(A-B) U (B-A) 6. Let A, B, and C be subsets of some universal set U. Prove or disprove each of the following: * (a) (A n B)-C = (A-C) n (B-C) (b) (AUB)-(A nB)=(A-B) U (B-A)
5. Verify the identities. Be sure to use correct vocabulary to justify your steps (cite the specific identities). (5 points each) b) 8 sin cos? 0 = 1- cos 40
8. Let A and B be subsets of some universal set U. From Proposition 5.10, we know that if A S B, then B S A. Now prove the following proposition: For all sets A and B that are subsets of some universal set U, A C B if and only if B S A.
Verify which of the following are identities. ) 16 sin2 -cos2- tan20 = 16tan Gcsc e 1 cos 2) 11COS Both the equations are identities Only the first equation is an identity None of the equations are identities Only the second equation is an identity Verify which of the following are identities. ) 16 sin2 -cos2- tan20 = 16tan Gcsc e 1 cos 2) 11COS Both the equations are identities Only the first equation is an identity None of the...
D Question 7 Let A and B be subsets of a universal set U with n (U)-32, n (A) = 11, n (B) = 17, and n (AUB) = 25. Compute n(A' nB) D Question 8 Let A and B be subsets of a universal set U with n (U)-32, n (A)-11, n (B)-17, and n (A U B)=25 Compute n (AUB).
1. Let S and T be subsets of the universal set U. Use the Venn diagram on the right and the given data below to determine the number of elements in each basic region. n(U)=25 n(S)=13 n(T)=14 n(SUT)=19 Region I contains _____ elements Region II contains _____ elements Region III contains _____ elements Region IV contains _____ elements ______________________________________________________________________________________________________ 2. Let R, S, and T be subsets of the universal set U. Use the Venn diagram on the right and...
A,C,G please 1. Let A, B, and C be subsets of some universal set u. Prove the following statements from Theorem 4.2.6 (a) AUA=/1 and AnA=A. (b) AUO- A and An. (c) AnB C A and ACAUB (d) AU(BUC)= (A U B) U C and An(B n C)-(A n B) n C. (e) AUB=BUA and A n B = B n A. (f) AU(BnC) (AU B) n(AUC) (g) (A U B) = A n B (h) AUA=1( and An-=0. hore...