Tuesday 27 November

With every implication there are three other statements that are associated.

If p \implies q then:

  • The inverse of p \implies q is ¬p \implies ¬q
  • The converse of p \implies q is p\Longleftarrow q or q \implies p
  • The contrapositive of p \implies q is ¬q \implies¬ p

You still use the words ”If…then…” from you propositions, but include ”not”, etc.

p. 248 8E 1a,b, 2,a,b. Then the examination questions, see post below.

  •  Remember: An implication is only False when the antecedent is True and the consequent is False.

Friday 23 November

Today we are going to go through implication and equivalence. You will also hear about the converse of an implication.

Learning goals:

  • Understand the concepts.
  • How to write them in symbols.
  • The truth table values for the concepts.

p. 246 8D

1 a,b, 2 a,b, 3 a,b, 4 a-c, 5 a, c, e

Wednesday 21 November

Today we will go through:

  • More of truth tables. Also with three propositions.
  • Logical equivalence – when you have the same T/F-values in two columns in a truth table.
  • Tautology – if all values in a truth table column are true.
  • Logical contradiction – if all values in a truth table column are false.

p. 242, 8C.1
2, b,c,d
7a

p. 244 8C.2
2

Friday 16 November

Today we are going to start the topic Logic, our 9th unit.

Logic deals with the conversion of worded statements into symbols and is the study of correct reasoning.

Logic involves many concepts which you have to learn. We are going to tick them off, one by one:

  • Proposition
  • Negation
  • Truth tables
  • Conjunction
  • Disjunction
  • Exclusive disjunction
  • Logical Equivalence
  • Tautology
  • Logical contradiction
  • Implication
  • Equivalence
  • Converse
  • Inverse
  • Contrapositive
  • Valid arguments

Today: Propositions, negation, conjunction and disjunction. And, an introduction of truth tables.

Propositions

– Statements that are either true or false.
– Use the notation p: or q: (or other letters, such as r and s)

Negation

– The negation of a proposition is ”not p”.

Conjunction

Join two propositions with the word and.

Disjunction

Join two propositions with the word or.

page 233, 8A.1 1-3, page 236, 8B.1, 1-3.

Wednesday 14 November

Today we will have our last lesson on calculus.

Next lesson we will do something completely different, Logic. Please watch the video below as an introduction: