. 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
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2. Let R, S, and T be subsets of the universal
set U. Use the Venn diagram on the right and...
10. Determine whether or not the following are valid. Justify your answer by using either set identities or membership tables. You must use membership tables at least once and vou must use set identities at least once . A, B, and C are sets. (a) (A-B) U (C-B) = (A U C)-B (b) (A-B) U (A-C) A-(B U C)