ANSWER 1-10, A. (11-14), AND B.(15-16)

Problem Set on Math Language and Logic

For nos. 1-3, translate the following sentences using mathematical symbols: 1. The average of three numbers is equal to 8. 2. The square of the sum of m and n is equal to p. 3. Six is the principal square root of 36. 4. Write the If - then form of this statement: The product of two even integers is an even integer. For nos. 5 -6, label the simple propositions using letters (ex. P, Q, R) then express each compound sentence using the correct logical connectives: 5. man 6. If a = b, then a + c= b + c For nos. 7 - 8, write the ff. statements in symbolic form: Let P: The sun is shining. Q: It is raining. R: The ground is wet. 7. If it is raining, then the sun is not shining. 8. The ground is wet if and only if it is raining and the sun is not shining. For nos. 9-10, Write each of the following as an English sentence and determine if it is True or False. 0 = X - XC 'ND ME 'ND XAI 0 = KE - X 'NBA 'x E ZA. Represent the simple propositions with the capital letters P, Q, or R, then express each compound sentence using the logical symbols: v ^, -, =>, and 11. If x is an odd number, then x + 1 is even. 12. If a = b, and b = c, then a = c. 13. The sun is shining or it is raining. 14. The ground is not wet. B. Give the CONVERSE, INVERSE and CONTRAPOSITIVE of the following implications. Make sure to label properly each statement according to the type of statement. ( 7 pts each) 15. There are no face-to-face classes in all levels if there is COVID-19 pandemic in the country. Converse: Inverse: Contrapositive: 16. I'm wearing face mask, only if I'm protecting myself from the virus. Converse: Inverse: Contrapositive