{"id":12909,"date":"2023-01-02T15:11:30","date_gmt":"2023-01-02T12:11:30","guid":{"rendered":"https:\/\/starlanguageblog.com\/?p=12909"},"modified":"2023-01-02T15:11:30","modified_gmt":"2023-01-02T12:11:30","slug":"why-is-aab-ab","status":"publish","type":"post","link":"https:\/\/www.starlanguageblog.com\/why-is-aab-ab\/","title":{"rendered":"Why is \u0100+AB = \u0100+B ?"},"content":{"rendered":"
\u0100+AB = \u0100+B because the terms AB and B are equal. This follows from the fact that A+A = A, which is one of the axioms of Boolean algebra.<\/p>\n
In Boolean algebra, A+A = A is known as the “absorption” or “idempotent” law. It states that the OR of a value with itself is equal to the value itself. Similarly, A*A = A is known as the “idempotent” law of AND.<\/p>\n
Here’s a proof that AB = B using the axioms of Boolean algebra:<\/p>\n
Here are some examples to illustrate the absorption law in Boolean algebra:<\/p>\n
A+A = A<\/p>\n
For example, if A represents the statement “It is raining outside,” then A+A would represent the statement “It is raining outside, OR it is raining outside.” This is clearly true, so A+A = A.<\/p>\n
AB+A = A<\/p>\n
For example, if A represents the statement “It is raining outside,” and B represents the statement “I have an umbrella,” then AB+A would represent the statement “It is raining outside AND I have an umbrella, OR it is raining outside.” This is also true, because if it is raining outside and I have an umbrella, then it is necessarily true<\/a> that it is raining outside. Therefore, AB+A = A.<\/p>\n AB+B = B<\/p>\n For example, if A represents the statement “It is raining outside,” and B represents the statement “I have an umbrella,” then AB+B would represent the statement “It is raining outside AND I have an umbrella, OR I have an umbrella.” This is true because if it is raining outside and I have an umbrella, then I have an umbrella (which is one of the terms being ORed). Similarly, if it is not raining outside, then having an umbrella is still true. Therefore, AB+B = B.<\/p>\n","protected":false},"excerpt":{"rendered":" Why is \u0100+AB = \u0100+B ? \u0100+AB = \u0100+B because the terms AB and B are equal. This follows from the fact that A+A = A, which is one of the axioms of Boolean algebra. In Boolean algebra, A+A = A is known as the “absorption” or “idempotent” law. It states that the OR of […]<\/p>\n","protected":false},"author":1,"featured_media":12910,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2078],"tags":[2084],"yoast_head":"\n