Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Question
Example 9 Truth Tables a. Construct a truth table for (p Aq) A (~rvq). b. Use the truth table from part a to determine the truth value of (pAq) A(-rvq) given that p is true, q is true, and r is false. Solution a. Using the procedures developed in Example 19, we can produce the following table. The shaded column is the truth table for (p A q) A (~rv q). The numbers in the squares below the columns denote the order in which the columns were constructed. pnq -rvq (pAq) A(-rV T T F T T row 1 T T F row 2 T F T F F row 3 PANGASINAN STATE UNIVERSITY 23 Study Guide in Muthematica in the Modem World FM-AA-CIA-15 Rev. O 10-July-2020 GE7 Mathematics in the Modern World Module 2: Mathematical Language and Symbol T F F T F row 4 F T F F F row 5 F F F F row 6 F F T F F F F row 7 F F T F row 8 b. In row 2 of the above truth table, we see that (p Aq) A (~ rvq) is true when p is true, q is true, and r is false. a. Construct a truth table for (~ pAr) v (q A~r) b. Use the truth table that you constructed in part a to determine the truth value of (~ par) v (q A -r)given that p is false, q is true, and r is false. Your turn 9
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Transcribed Image Text:Example 9 Truth Tables a. Construct a truth table for (p Aq) A (~rvq). b. Use the truth table from part a to determine the truth value of (pAq) A(-rvq) given that p is true, q is true, and r is false. Solution a. Using the procedures developed in Example 19, we can produce the following table. The shaded column is the truth table for (p A q) A (~rv q). The numbers in the squares below the columns denote the order in which the columns were constructed. pnq -rvq (pAq) A(-rV T T F T T row 1 T T F row 2 T F T F F row 3 PANGASINAN STATE UNIVERSITY 23 Study Guide in Muthematica in the Modem World FM-AA-CIA-15 Rev. O 10-July-2020 GE7 Mathematics in the Modern World Module 2: Mathematical Language and Symbol T F F T F row 4 F T F F F row 5 F F F F row 6 F F T F F F F row 7 F F T F row 8 b. In row 2 of the above truth table, we see that (p Aq) A (~ rvq) is true when p is true, q is true, and r is false. a. Construct a truth table for (~ pAr) v (q A~r) b. Use the truth table that you constructed in part a to determine the truth value of (~ par) v (q A -r)given that p is false, q is true, and r is false. Your turn 9
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