Chapter 1Part 1a

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Chapter 1-Part 1(a)

• Introduction to Logic

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Learning Objective

• Identify between the propositions and compound
  proposition.
• Differentiate and write the compound
  propositions.
• Differentiate and write the Propositional
  Equivalences.

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Propositions

• Logic
• Principles of reasoning, especially of the
  structure of propositions as distinguished from
  their content and of method and validity in
  deductive reasoning.
• It focuses on the relationship among statements
  as opposed to the content of any particular
  statement.

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Propositions

• Proposition
• Is a statement that is either TRUE or FALSE, but
  NOT BOTH

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Example

• Which of the following sentences is a
  proposition? Determine the truth value (true or
  false) of the sentence if it is a proposition.
• Kota Bahru is the capital city of Kelantan.
• Peel me a grape.
• Malaya became an independent nation on 31 August
  1957 and subsequently Malaysia on 16 September,
  1963.
• Keep off the grass!
• Bintulu is the capital city of Sarawak.
• 6 12 5 366
• Please be silent! You are in the Library!
• Earth is the only planet in the universe that
  contains life.

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Compound propositions

• 1. Negation
• 2. Conjunction
• 3. Disjunction
• 4. Exclusive Or
• 5. Implication
• 6. Biconditional

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Negation

• Let p be a proposition.
• The negation of p, denoted as p, read as
  not p.
• In other words this is not the case that p.
• The operator is a unary operator on
  propositions.
• The truth value of the proposition p is defined
  by the truth table

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Negation

• Example 1
• Let q Aminah is a student from Center for
  Diploma Programme, Multimedia University,
  Malacca.
• Answer
• Example 2
• Let r Maslina is a yoga instructor.
• Answer

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Conjunction

• Let p and q be propositions,
• The proposition of p and q, denoted by p q.
• The proposition that is true when both p and q
  are TRUE and is FALSE otherwise.
• The proposition p q is called a conjunction of
  p and q.

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Conjunction

• Example 3
• Let p Ali likes to swim. Let q Ali likes to
  jog.
• Answer
• QUESTIONS
• What is the truth value of propositions in
  example 3, if the p proposition is false?

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Disjunction

• Let p and q be propositions.
• The disjunction of p or q, denoted by p v q, is a
  compound proposition means p or q.
• Disjunction of p or q is the proposition that
  is FALSE when p and q are both false and TRUE
  otherwise.

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Disjunction

• Example 4
• Let p Muthu likes to eat. q Muthu likes to
  watch movies.
• Answer
• QUESTIONS
• What is the truth value of propositions in
  example 4, if the p proposition is false and the
  q proposition is true?

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Exclusive Or

• Let p and q be propositions.
• The exclusive or of p and q, is denoted by p
  q.
• Exclusive OR of p q is the proposition that
  is true when EXACTLY ONE of p and q is TRUE and
  is FALSE otherwise.

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Exclusive Or
Example 5

• Let p Muthu likes to eat. q Muthu likes to
  watch movies.
• Answer
• QUESTIONS
• What is the truth value of propositions in
  example 5, if both p and q propositions are
  false?

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Implication

• Let p and q be propositions.
• The implication of p and q, denoted by p?q, is a
  compound proposition that means if p then q.
• In this implication, p is called the hypothesis
  and q is called the conclusion (or consequence).

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Implication

• For an implication
• The converse of it is q ? p
• The contrapositive of it is q ? p
• The proposition of p ? q is called
  the inverse of p ? q.

• Example 6
• Let p Muthu likes to eat. q Muthu likes to
  watch movies.
• QUESTIONS
• 1. p?q
• 2. Converse
• 3. Contrapositive
• 4. Inverse

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Biconditional

• Let p and q be propositions.
• The Biconditional of p if and only if q,
  denoted by p q.
• The Biconditional for p q is TRUE when p and
  q have the same truth values, and is FALSE
  otherwise.

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Biconditional

• Example 7
• Let p Muthu likes to eat. q Muthu likes to
  watch movies.
• Answer
• QUESTIONS
• What is the truth value of propositions in
  example 7, if both p and q proposition are false?
  

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Tutorial

• Discrete Mathematics, 7th Edition
• Pg 20 21
• Question 2, 12, 18, 61
• Pg3031
• Question 32, 44, 45,52,53

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