Compound Propositions Quiz

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Questions and Answers

Why is it important to insert brackets in compound propositions?

  • To separate true and false values
  • To clarify the order in which connectives should apply (correct)
  • To simplify the proposition
  • To determine the number of truth values

What is a compound statement?

  • A statement that contains both true and false values
  • A statement formed by joining two or more propositions by connectives (correct)
  • A statement that is determined by systematic applications of rules
  • A statement that involves complex algebraic symbols

How many possible combinations of truth values are there for two propositions 𝑝 and 𝑞?

  • $2^4$
  • $2^2$ (correct)
  • $2^1$
  • $2^3$

How many rows would a truth table involving 'n' propositions have?

<p>$2^n$ (D)</p> Signup and view all the answers

If a compound proposition involves three propositions 𝑝, 𝑞, and 𝑟, how many possible combinations of truth values are there?

<p>$2^4$ (C)</p> Signup and view all the answers

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Study Notes

Importance of Brackets in Compound Propositions

  • Brackets clarify the order of operations, ensuring accurate interpretation of logical expressions.
  • They prevent ambiguity by indicating which propositions are grouped together, affecting the overall truth value.

Compound Statement Definition

  • A compound statement combines two or more simple statements using logical connectives (e.g., AND, OR, NOT).
  • Such statements can be evaluated as true or false based on the truth values of the individual components.

Truth Value Combinations for Two Propositions

  • Two propositions ( p ) and ( q ) can yield four possible combinations of truth values:
    • True (T) and True (T)
    • True (T) and False (F)
    • False (F) and True (T)
    • False (F) and False (F)

Truth Table Rows for 'n' Propositions

  • A truth table with 'n' propositions has ( 2^n ) rows.
  • Each row represents a unique combination of truth values for the propositions.

Truth Value Combinations for Three Propositions

  • For three propositions ( p ), ( q ), and ( r ), there are eight possible combinations of truth values:
    • All arrangements of T and F across the three propositions (2³ = 8).

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