I’m sure that you are used to hearing phrases like ”it’s only logical that the road is wet after it rains” or ”Amy has a logical idea.” In both phrases, the term logic seems to indicate something more that exists, and even though it has not been said it makes whatever stated fact reasonable. So can we say that logic is reasonable? Let’s find out!

### What is Logic?

Disciplines like mathematics, linguistics, law, physics, and computing all have logic in common. Therefore logic is not simply a field of study, but something that goes much further.

Logic has to do with the relationships between the language propositions we use to describe aspects of the world around us. It is important to understand that not every sentence is a proposition, **propositions are phrases that you can tell whether or not they are true.** For example, *‘Can you get me the salt?’* is not a proposition because there is no reason to confirm if *‘Can you get me the salt?’* is true. However *”the road is wet”* is a proposition because it can be determined to be true if there are puddles on it.

In particular,** logic is responsible for the study of the relationship of consequence between propositions.** But it does it in a very special, very “mathematical,” way. That is,** logic is limited to what the language says and not what the language shows.**

For example, imagine you come across a traditional math problem like the following:

No one would think of saying that maybe Charlie didn’t get to buy the candy, or that he lost some of the ones he had when he went to the kiosk. However, what does happen is you focus on the operations that appear explicitly in the word problem. That is 5 pieces plus 7 pieces of candy.

With logic, something similar happens when it comes to analyzing the consequence of some propositions. Now let’s understand what the consequence is all about!

### Logical Consequence and Its Importance

Let’s approach the notion of logical consequence by analyzing the following activity:

We are going to call the proposition **p,** ”it rained yesterday” and **q** *“Yesterday, Christina and her brother Nacho went to the movies together.” *The word problem is claiming **if p, then q**. Additionally, it is telling us that it did not rain yesterday, **not p**. The question is whether you can logically deduce from **not q** **if p**, **then q** and **not p**. The answer is no and we’re going to see why.

The most elementary form of logical reasoning that goes back in time to what is known as *modus ponendo ponens*, which is nothing more than what common sense dictates. If one thing involves another and the first one happens, then the second one does as well. Put in a more formal way

**if p, then q** and **p**, **q **can be deduced.

However, it is not true that **if p, then q** and **not p**, it is deduced that **not q**. Indeed, in the case of the example, Christina and Nacho may or may not have gone to the movies yesterday because the only thing the statement says is that if it rains, then they go. Instead, it doesn’t say anything about what they do or stop doing, on the days when it doesn’t rain.

Situations like the previous one reflect ”having logic.” In fact, logic returns to thought and reviews the relationships between what we know. Thus, it allows us to identify valid reasoning structures and detect those wrong ones that lead to false knowledge about the world around us. **The study of logic is vital to the well-rounded education of a child in order to develop their ability to correctly argue points as well as their critical thinking.**

We will leave you with some previous posts from the Smartick blog with more logic exercises that children can find during their daily sessions:

And… **if** you would like your child to develop their critical thinking skills while learning mathematics,** then** don’t hesitate to join the Smartick community. Click here to register!

Learn More:

- Logic Exercises at Smartick
- Logic Exercises at Smartick and a Math Riddle
- Learning Logic: Children’s Favorite Smartick Sessions
- Smartick Improves Student Performance with Smartick Coding
- Five Logic Exercises to Practice this Summer

- Addition With and Without Carrying - 12/31/2022
- Summer Review to Prevent Learning Loss - 06/23/2022
- Direct and Inverse Proportionality Problems - 08/31/2021