Introduction to logic

Season 1 • Episode AP05 • Introduction to logic

Introduction to logic

Season 1

Episode AP05 Time frame 1 period

Prerequisites :

Objectives :

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Materials :

•

•

•

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1 – Matching game ^{10 mins}

Eah student in the lass is given a ard with an impliation on it. Students mingle to

nd :

1. rst, the onverse of their impliation;

2. seond, the ontrapositiveof their impliation.

Using aslideshow, the teaher introdues the voabulary of logi.

2 – True or not 10 mins

Students gather in groups of 4 : an impliation, its onverse, its ontrapositive and the

onverseofthe ontrapositive.Together, theydisusswhihonesofthe foursentenesare

true.

3 – Exercises Remaining time

Stillworking ingroups, students have to solve afew exerises about impliation.

Introduction to logic

Season 1

Episode AP05 Document Answer sheet

Your four implications

Type Sentence True ?

Impliation

Contrapositive

Converse

Contrapositive

of the

onverse

Exercises

Exerise 1

Foreah ofthe followingimpliations,writeits onverse then deideif the initalimplia-

tion is true and if the onverse is true.

Type Sentence True ?

Impliation If atriangle

ABC

[AB]

then it'sright-angledin

C

Converse

Impliation Ifa linepasses through the midpointsof twosides of a triangle,

then it'sparallel tothe third side.

Converse

Season 1 • Episode AP05 • Introduction to logic

Type Sentence True ?

Impliation If atriangle has analtitude that isalso amedian,

then it'sisoseles.

Converse

Impliation If two altitudesof a trianglemeet in apoint

H

then the third altitude alsopasses through

H

Converse

Impliation If aprodut is equalto

0

then at least one of the terms isequal to0.

Converse

Exerise 2

For eah pair of statements

p

q

p

q

2 p ⇒ q 2 q ⇒ p 2 p ⇔ q 2 ¬p ⇒ ¬q 2 ¬q ⇒ ¬p p

q

19

2 p ⇒ q 2 q ⇒ p 2 p ⇔ q 2 ¬p ⇒ ¬q 2 ¬q ⇒ ¬p p

CDEF

q

CDEF

2 p ⇒ q 2 q ⇒ p 2 p ⇔ q 2 ¬p ⇒ ¬q 2 ¬q ⇒ ¬p

p

x ∈

q

x ∈

2 p ⇒ q 2 q ⇒ p 2 p ⇔ q 2 ¬p ⇒ ¬q 2 ¬q ⇒ ¬p p

M N P

M

q

M P ² + M N ² = N P ²

2 p ⇒ q 2 q ⇒ p 2 p ⇔ q 2 ¬p ⇒ ¬q 2 ¬q ⇒ ¬p

p

x ≥ −2

q

x ≥ −1

2 p ⇒ q 2 q ⇒ p 2 p ⇔ q 2 ¬p ⇒ ¬q 2 ¬q ⇒ ¬p p

a + b = 5

q

a = 2

b = 3

2 p ⇒ q 2 q ⇒ p 2 p ⇔ q 2 ¬p ⇒ ¬q 2 ¬q ⇒ ¬p p

4x − (x + 5) = 7

q

x = 4

2 p ⇒ q 2 q ⇒ p 2 p ⇔ q 2 ¬p ⇒ ¬q 2 ¬q ⇒ ¬p p

n

q

n

3

2 p ⇒ q 2 q ⇒ p 2 p ⇔ q 2 ¬p ⇒ ¬q 2 ¬q ⇒ ¬p p

(ax + b)(cx + d) = 0

q

ax + b = 0

cx + d = 0

2 p ⇒ q 2 q ⇒ p 2 p ⇔ q 2 ¬p ⇒ ¬q 2 ¬q ⇒ ¬p

Document 1

If the triangle

ABC

A

BC ² = AB ² + AC ²

If

BC ² = AB ² + AC ²

ABC

A

If the triangle

ABC

A

BC ² 6= AB ² + AC ²

If

BC ² 6 = AB ² + AC ²

ABC

A

If a quadrilateral is a square,

then its diagonals have the same length.

If the diagonals of a quadrilateral have the same length,

then it's a square.

If a quadrilateral is not a square,

then its diagonals don't have the same length.

If the diagonals of a quadrilateral don't have the same length,

then it's not a square.

If

x

x ² = 9

x = 3

If

x

x = 3

x ² = 9

If

x

x ² 6 = 9

x 6 = 3

Season 1 • Episode AP05 • Introduction to logic

If

x

x 6= 3

x ² 6= 9

If the median of a statistial set of data is

12

then at least

50%

12

If at least

50%

12

then the median of a statistial set of data is

12

If the median of a statistial set of data is not equal to

12

then less than

50%

12

If less than

50%

12

then the median of a statistial set of data is not equal to

12

If a triangle is equilateral, then it's right-angled.

If a triangle is right-angled, then it's equilateral.

If a triangle is not equilateral, then it's not right-angled.

If a triangle is not right-angled, then it's not equilateral.