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Number of  rows appear in the truth table for this compound proposition  (p ∧ r ∧ s) ∨  (r ∧ ¬ t) equal 8.Group startsTrue or FalseTrue, unselectedFalse

Question

Number of rows appear in the truth table for this compound proposition

(p ∧ r ∧ s) ∨ (r ∧ ¬ t) equal 8.
Group starts
True or False
True, unselected
False

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Solution

To determine the number of rows in the truth table for the compound proposition (prs)(r¬t)(p \land r \land s) \lor (r \land \neg t), we first need to identify the distinct variables involved and the logic behind how truth tables are constructed.

Break Down the Problem

  1. Identify the variables in the expression:
    • The expression has the variables pp, rr, ss, and tt.
  2. Count the distinct variables:
    • The distinct variables are p,r,s,tp, r, s, t, totaling 4 variables.

Relevant Concepts

  1. The number of rows in a truth table is determined by the formula 2n2^n, where nn is the number of distinct variables.

Analysis and Detail

  1. Applying the formula:
    • Here, n=4n = 4 (since we have 4 distinct variables: pp, rr, ss, and tt).
    • Therefore, the number of rows is: 24=16 2^4 = 16

Verify and Summarize

  1. The options presented were either "True" or "False". The claim was that the number of rows equals 8. Since we calculated that the number of rows actually equals 16, we conclude that the statement is False.

Final Answer

The statement "the number of rows appear in the truth table for this compound proposition equals 8" is False. The correct number of rows is 16.

This problem has been solved

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