Question 7 QS T T T F FT F F Complete the truth table for the statement -QA-S. -QA-S ? ? B ?C ? 6 Question Help: Video ( Check Answer >
Question 7 QS T T T F FT F F Complete the truth table for the statement -QA-S. -QA-S ? ? B ?C ? 6 Question Help: Video ( Check Answer >
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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### Explanation:
In this truth table, we are working with the logical statement `¬Q ∧ ¬S`. The table requires us to fill in the values for ¬Q, ¬S, and ¬Q ∧ ¬S based on the combinations of truth values for Q and S provided in the table.
- **¬Q**: This is the negation of Q. So, if Q is true (T), ¬Q will be false (F) and vice versa.
- **¬S**: This is the negation of S. So, if S is true (T), ¬S will be false (F) and vice versa.
- **¬Q ∧ ¬S**: This is the logical AND operation between ¬Q and ¬S. This statement is true only if both ¬Q and ¬S are true.
Let's fill in a sample truth table:
| Q | S | ¬Q | ¬S | ¬Q ∧ ¬S |
|------|------|------|------|---------|
| T | T | F | F | F |
| T | F | F | T | F |
| F | T | T | F | F |
| F | F | T | T | T |
In Row 1:
- Q = T, S = T
- ¬Q = F,](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa6fffe07-0182-49b4-949f-7de773e92073%2F5dcbd0d0-2391-4aef-bde4-93a94aa3be77%2Frv89t9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:## Truth Table for Logical Statement
**Exam 1 (Chapters 1-3)**
**Score: 16.2/21**
**18/21 answered**
### Question 7: Complete the Truth Table for the Statement `¬Q ∧ ¬S`
#### Truth Table:
| Q | S | ¬Q | ¬S | ¬Q ∧ ¬S |
|------|------|------|------|---------|
| T | T | ? | ? | ? |
| T | F | ? | ? | ? |
| F | T | ? | ? | ? |
| F | F | ? | ? | ? |
**Question Help:**
- [Video](#)
**Action Button:**
- [Check Answer](#)
### Explanation:
In this truth table, we are working with the logical statement `¬Q ∧ ¬S`. The table requires us to fill in the values for ¬Q, ¬S, and ¬Q ∧ ¬S based on the combinations of truth values for Q and S provided in the table.
- **¬Q**: This is the negation of Q. So, if Q is true (T), ¬Q will be false (F) and vice versa.
- **¬S**: This is the negation of S. So, if S is true (T), ¬S will be false (F) and vice versa.
- **¬Q ∧ ¬S**: This is the logical AND operation between ¬Q and ¬S. This statement is true only if both ¬Q and ¬S are true.
Let's fill in a sample truth table:
| Q | S | ¬Q | ¬S | ¬Q ∧ ¬S |
|------|------|------|------|---------|
| T | T | F | F | F |
| T | F | F | T | F |
| F | T | T | F | F |
| F | F | T | T | T |
In Row 1:
- Q = T, S = T
- ¬Q = F,
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