Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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## 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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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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