Tuesday 8 January

Welcome back to school!

In Onenote you can find the plan for week 2 – 10.

In Sharepoint you can find summaries for every topic included in the syllabus.

Today we will go through two examination questions involvning:

– Pythagoras Theorem
– Right angled trigonometry
– Non-right angled trigonometry

The questions can be found in Sharepoint, question 2 and 3.

Remember:

  • Pythagoras Theorem can only be applied on right angled triangles, and only to find length of a side.
  • ”SOH CAH TOA” can only be applied on right angled triangles, and involves relations between angles and length of sides.
  • Sine rule and Cosine rule are applied on non-right angled triangles.
    • Use Sine rule, when given:
      – Two angles and one side (to find length of another side). (If you know two angles, you also know the third…)
      – Two sides and a non-included angle (to find the size of another angle).
    • Use Cosine rule when given:
      – Two sides and an included angle (to find the length of the third side).
      – Three sides (to find the size of an angle).

Wednesday 28 November

Valid Arguments

An argument consists of a premise and a conclusion.
If the truth table for an argument leads to a tautology, then the argument is valid.
Example:
Consider the following propositions…:
p: It rains
q: You stay indoors
And their negations:
¬p: It does not rain
¬q: You do not stay indoors
From these propositions I have constructed the following argument:
If it rains then you stay indoors.
It does not rain.
             Therefore, you do not stay indoors.
”If it rains then you stay indoors.
It does not rain”. – The premise.
            ”Therefore, you do not stay indoors.” – The conclusion.
The argument in symbols:
p \implies q
¬p
———————
¬q
What we need to show in a truth table is:
(p \implies q) ∧ ¬p \implies ¬q
to state whether it is a valid argument or not.
 P. 255, review set 8B, 7a. Then logic examination questions or revision exercises.

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.