Write the First-Order Logic of the following: (Hint: you may need to use the Symbols: vx, 3x, ^, ¬, V) 1. John is the father of Mike. 2. Kate is the mother of Sara. 3. Sara is married. She has 1 boy and 1 girl.
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- 3. Write the First Order Logic of the following: (Hint: you may need to use these symbols: Vx, 3x, A, 7, V) (a) Tim and Mike like to play FIFA, Mike beats Tim. (b) All Muslims go to Mosques. (c) Some kids like to go to Disney Land and other kids likes to go to Lego Land. (d) Kuala Lumpur is the capital city of Malaysia. (e) Only one student missed the quiz and the final exam. (f) All the students in ITIB3914 class are intelligent. (g) Mike likes Al class and does not like math class. (h) John is the father of Mike. (i) Kate is the mother of Sara. (i) John and Kate are parents.Question V Represent the following statements in first-order logic, using the following vocabulary: Person(x): x is a person IsAVegetable(y): y is a vegetable IsAFruit(z): z is a fruit Likes(u,v): u likes v 1. Every person likes some vegetable. 2. There is a person who likes all vegetables or likes some fruit. 3. Every person likes all fruits but does not like some vegetable. 4. There is a person who likes exactly one vegetable. Full explain this question and text typing work only We should answer our question within 2 hours takes more time then we will reduce Rating Dont ignore this line1. Write the negation of the statements below. a. If the glass is empty, then there is no water. b. The division of two integer nonzero numbers is rational. 2. Write the statement in the formal form, then write its converse, inverse and contrapositive and negation statements for the given statement below. "People, who exercise every day, will stay fit."
- 3. Write the First Order Logic of the following: (Hint: you may need to use these symbols: Vx, 3x, A, , V) (a) Tim and Mike like to play FIFA, Mike beats Tim. (b) All Muslims go to Mosques. (c) Some kids like to go to Disney Land and other kids likes to go to Lego Land.Question:: write out the four logical forms of the statement: Cats make great pets.(Lable the four forms: Statement, inverse, etc. and write them as if.. then..)Four mathematicians have a conversation, as follows: ALICE: I am insane. BOB: I am pure. CHARLES: I am applied. DOROTHY: I am sane. ALICE: Charles is pure. BOB: Dorothy is insane. CHARLES: Bob is applied. DOROTHY: Charles is sane. You are also given the following information: Pure mathematicians tell the truth about their beliefs. Applied mathematicians lie about their beliefs. Sane mathematicians' beliefs are correct. Insane mathematicians' beliefs are incorrect. With the preceding clues, classify the four mathematicians as applied or pure, and insane or sane. Briefly explain your logic.
- 5) Let's say you and your friend are trying to predict the outcome of a flip of a coin. In MATLAB, create a random coin flip with heads being 1 and tails being 2. Ask the user to predict what the outcome will be. If the user predicts right, display a winning sentence and vice versa for if the user does not predict right. Afterwards, ask the user if they want to play again or stop playing. If the user elects to play again, the program should run itself from the beginning asking the user for their prediction.Directions: Identify the propositions among the given statements. Write P if the statement is a proposition, and NP if not. Give the truth value of the propositions (T or F). (Use a comma as a separator of P and T or F. For instance, P,T .) 1. How far is Unitop from NCCC? 2. Orange is a tertiary color. 3. x - 2 = 2x, when x = -2. 4. You made it! 5. Iran is a country in the Middle East. 6. There are 31 days in December. 7. How are you feeling? 8. Don’t speak when your mouth is full. 9. Mixing blue and yellow produces red. 10. 2x + 1 = 5.Doming, Melvin, and Sebastian could each be a dancer, a mechanic, or a singer. None has a job that starts with the same letter as his name. Doming recently has his car repaired by the mechanic. Who has which job? A. Doming is the singer, Melvin is the dancer, and Sebastian is the mechanic. B. Doming is the mechanic, Melvin is the singer, and Sebastian is the dancer. C. Doming is the dancer, Melvin is the singer, and Sebastian is the mechanic. D. Doming is the singer, Melvin is the mechanic, and Sebastian is the dancer.
- Write the converse, inverse, and contrapositive of the following statements- 1] The given sentence is- “If you are intelligent, then you will pass the exam.”This sentence is of the form- “If p then q”. 2] The given sentence is- “You will qualify GATE only if you work hard.”This sentence is of the form- “p only if q”.i. Marcus was a man. ii. All man are person.iii. Marcus was a Pompeian. iv. All Pompeians were Romans.v. Caesar was a ruler. vi. All Pompeians were either loyal to Caesar or hated him.vii. Everyone is loyal to someone. viii. People only try to assassinate rulers they are not loyal to. ix. Marcus tried to assassinate Caesar. Convert the following sentences into first order logic. And analyzing the above sentence answer and reason “Was Marcus loyal to Caesar?”Refer to the following statement to answer parts (a) through (c) below, The professor is intelligent and an overachiever, or not an overachiever a. Write the statement in symbolic form Assign letters to simple statements that are not negated Choose the correct answer below OA. let p=The professor is intelligent and letq= The professor is not an overachiever, (p A q)v OB. let p= The professor is intelligent and let q= The professor is not an overachiever (p v q) A OC. let p= The professor is intelligent and let q= The professor is an overachiever (p A q) v -q O D. letp=The professor is intelligent and let q= The professor is an overachiever, (p v q) ^ -9 b. Construct a truth table for the symbolic statement in part (a) PAq (pAq) v -q T.