a. Construct a truth table for (pAr) V (q ^-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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10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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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
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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