Subj: Math

solve the following questions ( handwritten) solution only neatly and clean it must be complete read instructions.

A. In Lily's flower garden, she observed the following rules in planting her lilies. 1. There is at least one row. A row is determined by a 6-inch smooth-curve path. 2. Each row has exactly three lily bulbs on it 3. Not all bulbs are on the same row. 4. Each two bulbs are on exactly one row. 5. Each two rows have at least one bulb on both of them. Such rules constitute a set of axioms for an axiomatic system (Lily's flower garden). a) Identify the undefined terms in the axiomatic system. Classify each term as to whether it is an element or a relation. [3 points] b) Show that the axiomatic system is consistent by constructing an interpretation that gives a concrete model for the system. [2 points for a correct interpretation, 2 points for a correct model] c) How many lily plants in all did Lily grow in her flower garden? [2 points] d) How many rows are there that have one lily plant on all of them? [2 points] Is this number the same for every lily plant in the garden? [1 point] B. Given the statement: A prime number is a number that is not composite. A composite number is a number that is not prime. 1. Does the statement accurately define the given word or phrase? [1 point] 2. If not, identify whether the statement is circular or is not characteristic. [1 point] 3. If the statement is not characteristic, give an example that fits the given description but not the word or phrase described, or vice versa. If it is circular, explain why it is so. [1 point] C. Consider the numerical data given below. 1. Verify that each is true. [2 points] 2. Take a closer look at these facts and based on your observation, write an abstraction (a general form of equation) about the behavior of the numbers. [2 points] 23 - 13 + 3 (2)(1)2 = (2- 1)3 + 3(2)3(1) (2) -13+ 3 () (1)= =(2-1) +3() 33 - (-1)3 + 3 (3)(-1)? = 13 -(-1)]3 +3(3)=(-1)