Showcase - Logic

Showcase - Logic

Author: EduPlexor

Introduction

In logic we mostly deal with statements.

What exactly is a statement?

In short, we could say that this is an informative phrase, that is, a phrase that conveys a certain information. The main characteristic of a statement is that it can be either correct or incorrect.

You will learn more about statements logic from Albert, Mandy and Jake.

(/files/103/mandy_albert_jake.png)

Exercise

Consider the following statement.

  • Jaka will make a snowman, if and only if there is enough snow outside.

We know that Jaka made a snowman. What follows from this statement?

(/files/103/jaka_snezak.png)
Outside the sun is shining and it is practicaly already spring.
There is enough snow outside.
Jake went skiing.
It is raining.

Think about it! When we use "if and only if" in the sentence, both partial sentances must be correct for the entire sentence to be correct.

Next

That's right! When we use "if and only if" in the sentence, both partial sentances must be correct for the entire sentence to be correct.

Grid puzzle

Project-Id-Version: PROJECT VERSION
Report-Msgid-Bugs-To: EMAIL@ADDRESS
POT-Creation-Date: 2011-04-12 10:21+0200
PO-Revision-Date: 2012-10-16 10:59+0200
Last-Translator: Iztok <iztok@abelium.eu>
Language-Team: Abelium
Plural-Forms: nplurals=4; plural=(n%100==1 ? 0 : n%100==2 ? 1 : n%100==3 || n%100==4 ? 2 : 3)
MIME-Version: 1.0
Content-Type: text/plain; charset=utf-8
Content-Transfer-Encoding: 8bit
Generated-By: Babel 0.9.4
first click
Project-Id-Version: PROJECT VERSION
Report-Msgid-Bugs-To: EMAIL@ADDRESS
POT-Creation-Date: 2011-04-12 10:21+0200
PO-Revision-Date: 2012-10-16 10:59+0200
Last-Translator: Iztok <iztok@abelium.eu>
Language-Team: Abelium
Plural-Forms: nplurals=4; plural=(n%100==1 ? 0 : n%100==2 ? 1 : n%100==3 || n%100==4 ? 2 : 3)
MIME-Version: 1.0
Content-Type: text/plain; charset=utf-8
Content-Transfer-Encoding: 8bit
Generated-By: Babel 0.9.4
second click
Project-Id-Version: PROJECT VERSION
Report-Msgid-Bugs-To: EMAIL@ADDRESS
POT-Creation-Date: 2011-04-12 10:21+0200
PO-Revision-Date: 2012-10-16 10:59+0200
Last-Translator: Iztok <iztok@abelium.eu>
Language-Team: Abelium
Plural-Forms: nplurals=4; plural=(n%100==1 ? 0 : n%100==2 ? 1 : n%100==3 || n%100==4 ? 2 : 3)
MIME-Version: 1.0
Content-Type: text/plain; charset=utf-8
Content-Transfer-Encoding: 8bit
Generated-By: Babel 0.9.4
third click
5
6
8
December
June
May
Andy
Jake
Matt
December
June
May

Mr. and Mrs. Novak have three children aged 5, 6 and 8 years. One of them was born in May, one in June, one in December.

Determine the age and month of birth for all three children. In the following table you can find all the options for each of the categories.

NameAgeMonth of birth
Andy5December
Jake6June
Matt8May

Good luck! Before you start, take a look at the list of facts.

  1. Matt doesn't like that his birthday coincides with Christmas.
  2. Jake can count his age with fingers on one hand.
  3. Andy was born in May.
  4. Matt is 6 years old.
NameAgeMonth of birth
Andy5December
Jake6June
Matt8May

The following answers have been determined from your entries in the grid:
Name Age Month of birth
Andy
Jake
Matt

Well done! You have filled the grid completely. If you are satisfied with the answers, press the button bellow:

How to solve:

To solve the task, you have to fill the upper 3 rows in the grid on the left. Put the red X to the wrong and green circle to the correct combinations. Click once to set the red X and again to set the green circle. Click the third time to clear the place.

Every time you mark a combination with green circle, it will show up among your answers. When all the answers are set and you are convinced that the combinations are correct, you can press the button to check the solution.


Hints:

If you have no idea what to do next, press the button below to get a hint.

Hint no. (number): (hint text)

Determine the validity of statements about the two worlds.

(/files/103/svetovi_031.png) (/files/103/svetovi_032.png)
World 1 2
1.
Shape A is a pentagon and shape E is gray.
2.
Shape A isn't a pentagon and shape E isn't gray.
3.
Shape A is a pentagon or is shape E gray.
4.
Shape A is a pentagon or shape E isn't gray.
5.
Shape A isn't a pentagon or shape E isn't gray.
6.
Either is shape A a pentagon or is shape E gray.
7.
Either shape A isn't a pentagon or shape E isn't gray.
8.
If shape A isn't a pentagon, then shape E isn't gray.
9.
Shape A is a pentagon, if and only if is shape E gray.

Mark the propositions in the grid as true or false according to the pictures of the worlds.

Click to mark propositions as follows:

first click
second click
third click

The number of correct answers is 0 out of 0.

Latin squares

In the 5 x 5 squares type natural numbers from 1 to 5, so that in each row and each column operate at all five numbers.

Exercise

Which two statements describe the picture on the right?

Check

(/files/103/jaka_sonce.png)

Think about it! Statements must describe the actual facts!

Next

That's right! We see Jake writing a letter with the sun shining outside.

Next

Kakuro

Fill in the white squares with digits from 1 to 9 so that the sum of digits in consecutive white squares across the rows and columns equal to the number that is written in the black box at the beginning of the line (column) over the (sub) diagonal. In doing so, however, all digits in each row (column) are different.

Negation

Find a negation of the following terms:

Jaka is a good athlete.
Albert has six brothers.
Today is Tuesday.
Albert is a good mathematician.
It is not true that Jaka a good athlete.
Albert doesn't have six brothers.
Today is not Tuesday.
Albert isn't a good mathematician.
Albert has 3 brothers.
Jaka is not a good skier.
It is not true, that Jaka is not a good athlete.
Today is Wednesday.
Tomorrow is Thursday.
Albert is a good logician.

Check

Answers are not correct. Try again!

Again

Excellent! You have successfully solved the task!

Next

Futoshiki

In the 4 x 4 grid squares type natural numbers from 1 to 4, so that each row and each column appeared four numbers, and that will satisfy all the relations.

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Color sudoku

In the 4 x 4 grid squares type natural numbers from 1 to 4, so that each row in each column and in the squares of the same color appeared all four numbers.

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