P T a T 9 r F b F LL F C LL qvr 0 ~C 0 ~ (qvr) 0 a^~c 0 ~ (qvr) ^p 0 ~(a^~c) bra 0 X S ~(a^~c) v(bna) 0
P T a T 9 r F b F LL F C LL qvr 0 ~C 0 ~ (qvr) 0 a^~c 0 ~ (qvr) ^p 0 ~(a^~c) bra 0 X S ~(a^~c) v(bna) 0
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:### Logic: Completing Rows of Truth Tables - Conjunctions and Disjunctions
**Task Instructions:**
Complete the row of each truth table. Use T for true and F for false.
#### Truth Table 1:
| p | q | r | q ∨ r | ~(q ∨ r) | ~(q ∨ r) ∧ p |
|---|---|---|-------|---------|-------------|
| T | F | F | | | |
#### Truth Table 2:
| a | b | c | ~c | a ∧ c | ~(a ∧ c) | b ∧ a | ~(a ∧ c) ∨ (b ∧ a) |
|---|---|---|----|-------|----------|-------|--------------------|
| T | F | F | | | | | |
**Explanation:**
In this task, you are required to fill in the missing values in the truth tables based on the given logical expressions.
1. **Truth Table 1:**
- Columns `p`, `q`, and `r` represent the initial truth values.
- Column `q ∨ r` is the disjunction (logical OR) of `q` and `r`.
- Column `~(q ∨ r)` represents the negation of the result from `q ∨ r`.
- Column `~(q ∨ r) ∧ p` is the conjunction (logical AND) of `p` and the result from `~(q ∨ r)`.
2. **Truth Table 2:**
- Columns `a`, `b`, and `c` represent the initial truth values.
- Column `~c` is the negation of `c`.
- Column `a ∧ c` is the conjunction (logical AND) of `a` and `c`.
- Column `~(a ∧ c)` represents the negation of the result from `a ∧ c`.
- Column `b ∧ a` is the conjunction (logical AND) of `b` and `a`.
- Column `~(a ∧ c) ∨ (b ∧ a)` is the disjunction (logical OR) of the results from `~(a ∧ c)` and `b ∧ a`.
Once the values are correctly filled, you can
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