Discrete math

Propositions The complete objects we operate with In arithmetical ar numbers. In a similar way, the fundamental objects In logic are propositions. Definition A proposition Is a statement that is either au thereforetic or false. Whichever of these (true or false) is the case is called the truth care for of the proposition. Here are some examples of English dooms that are propositions Canberra is the capital of Australia. There are 8 days in a week. Isaac Newton was natural In 1642. 5 Is greater than 7. Every purge number greater than 2 can be expressed as the sum of two crown numbers. The following sentences are not propositions Where are you expiry? Come here. This sentence Is false. Explanation The first sentence is a question and the second is a command, so clearly neither is a proposition and the third gear sentence is rather more subtle. The study of the grammatical construction of compound propositions is made easier by the use of symbols for atomic propositi ons and connectives.We impart use lower-case letters such as p, q and r to denote atomic propositions. There are five connectives that we will use in our work they are listed in Table, together with their symbols. The If then and if and scarce if connectors will be our next topic on Monday. Express the following propositions in symbolic form, and call the principal connective (a) Either Karen Is studying figure and miniskirt Is not studying mathematics, or Mini Is studying mathematics. ) It Is not the case that If It Is sunny then I will carry an umbrella. (c) The program will terminate if and only if the input is not numerical or the escape key is pressed.