Example related to propositions

 

Examples Related to Propositions

A proposition is a declarative statement that is either true (T) or false (F) but not both.

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1. Simple Propositions

• Example 1: "The sun rises in the east." (True)
• Example 2: "5 is a prime number." (False)

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2. Compound Propositions

Compound propositions are formed using logical connectives: AND (∧), OR (∨), NOT (¬), IMPLIES (→), BICONDITIONAL (↔)

Example 1: Conjunction (AND, ∧)

• Statement: "It is raining AND it is cold."
• Symbolic Form: $P \wedge Q$
• Truth Table:

  P (Raining)	Q (Cold)	$P \wedge Q$
  T	T	T
  T	F	F
  F	T	F
  F	F	F

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Example 2: Disjunction (OR, ∨)

• Statement: "It is Monday OR it is Tuesday."
• Symbolic Form: $P \vee Q$
• Truth Table:

  P (Monday)	Q (Tuesday)	$P \vee Q$
  T	T	T
  T	F	T
  F	T	T
  F	F	F

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Example 3: Implication (→)

• Statement: "If it rains, then the ground is wet."
• Symbolic Form: $P \rightarrow Q$
• Truth Table:

  P (Rains)	Q (Ground Wet)	$P \rightarrow Q$
  T	T	T
  T	F	F
  F	T	T
  F	F	T

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Example 4: Negation (NOT, ¬)

• Statement: "It is NOT raining."
• Symbolic Form: $\neg P$
• Truth Table:

  P (Raining)	$\neg P$ (Not Raining)
  T	F
  F	T

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3. Logical Equivalence (Biconditional, ↔)

• Statement: "You can enter if and only if you have a ticket."
• Symbolic Form: $P \leftrightarrow Q$
• Truth Table:

  P (Have Ticket)	Q (Can Enter)	$P \leftrightarrow Q$
  T	T	T
  T	F	F
  F	T	F
  F	F	T

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These are fundamental examples of propositions used in logic, mathematics, and computer science for reasoning and problem-solving