# All Labrador retrievers bark a great deal. All Saint Bernards bark infrequently. Each of Rosa's dogs is a cross betwe...

Jessica on August 9 at 07:37AM

I don't understand what sufficient and necessary conditions are, and what they are in relation to this problem.

I am very confused. I don't know what a necessary or sufficient condition is. Is it sufficient if it says the word "all" always? And if so what does that mean? So the sufficient conditions are the ones with the 'all' and the necessary condition is what the sufficient conditions are combined? Or what they result in? I am so confused.

2 Replies

Shunhe on August 10 at 05:22PM

Hi @JessW,

Thanks for the question! So there’s a sufficient/necessary module I highly recommend you look at, but I’ll give you a brief overview here.

When we speak, we often use something called “conditional statements.” If some condition is met, then something else happens; these can all be expressed as if-then statements. If you press that red button, then the building will blow up. If it’s raining outside, then I’ll take my umbrella. Things like that.

The “if” condition is the one we refer to as the “sufficient condition,” and the “then” condition is the “necessary condition.” The “if” condition is called the sufficient condition because if it’s true, then the necessary condition is true. In other words, its truth is “sufficient” by itself for the truth of the necessary condition.

The “then” condition is called the necessary condition because it must be true for the “if” condition to be true. If it’s false, then the sufficient condition can’t have happened, since if the sufficient condition had happened, the necessary condition would’ve happened too. So going back to the red button building blowing up example. If the building didn’t blow up, then I didn’t press the red button, since if I had pressed the red button, the building would’ve blown up. So “the building blew up” must be true (is necessary) for “I pushed the button” to be true, which is why it’s called the “necessary” condition.

We use different words in English to introduce different conditions. As I’ve mentioned, “if” introduces sufficient. You also mentioned “all,” which also introduces sufficient. Other words, like “only,” introduce necessary. So that’s just a general overview; again, would highly suggest the sufficient/necessary module for more guidance on this.

Hope this helps! Feel free to ask any other questions that you might have.

Jessica on August 10 at 10:40PM

Thank you! This was incredibly helpful!