1st.pdf - University of the Philippines Manila College of Arts and Sciences Department of Physical Sciences and Mathematics MATHEMATICS 11 COLLEGE

1st.pdf - University of the Philippines Manila College of...

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University of the Philippines, Manila College of Arts and Sciences Department of Physical Sciences and Mathematics MATHEMATICS 11: COLLEGE ALGEBRA First Departmental Exam January 22, 2014 I.TRUE or FALSE.WriteTRUEif the given statement is accurate; otherwise, writeFALSE. (2 pts each)1. IfAandBare disjoint finite sets, then (2A×2B)2AB.2. The setR-(Q-Z) is closed under addition.3. IfzZ- {1}, thenzhas no multiplicative inverse.4. For any non-empty setA,{} ⊆2A5. If 2n(A)= 4 and 2n(B)= 8, thenABhas five elements.6. The expressionx4+kx2+ 1, wherekN, can only be factored if and only ifk=±2.7. Ifa, b,andcare non-zero real numbers such thatab > bc, thena > c.8. IfAandBare sets such thatn(2AB) = 0, then eitherAorBis empty.9. The setQ-Nis not a field under addition and multiplication.10. For any real numberα,α(1α)= 1.II.IDENTIFICATION. Provide thefinal answersto the following questions. (3 pts each)1. LetAandBbe any sets. Define the set differenceA-B.2. Draw a Venn-diagram representing set: [(A-
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