Determine the truth value of the following propositions: a) p: 2+3+5= 13 and 4+8 > 5+6 b) q: 9 is an even number and is not greater than 6 c) r: 18 is multiple of 3 but 5 is not greater than 8 d) s: It is not the case that 10 is a multiple of 3 or that 5+4 < 10 e) t: Mariano Melgar was a writer as well as a musician

To determine the truth value of the given propositions, we will evaluate each part separately.

a) p: 2+3+5=13 and 4+8>5+6

Step 1: Evaluate the left-hand side of the conjunction (AND operator):
$$2+3+5=10$$

Step 2: Evaluate the right-hand side of the conjunction (AND operator):
$$4+8>5+6$$
$$12>11$$

Step 3: Evaluate the truth value of the conjunction:
Since both the left-hand side and the right-hand side of the conjunction are true, the whole statement is true.

Answer: The truth value of proposition p is true.

b) q: 9 is an even number and is not greater than 6

Step 1: Evaluate the left-hand side of the conjunction (AND operator):
$$\text{9 is an even number}$$
This statement is false since 9 is an odd number.

Step 2: Evaluate the right-hand side of the conjunction (AND operator):
$$\text{9 is not greater than 6}$$
This statement is also false since 9 is indeed greater than 6.

Step 3: Evaluate the truth value of the conjunction:
Since one of the statements in the conjunction is false, the whole statement is false.

Answer: The truth value of proposition q is false.

c) r: 18 is a multiple of 3 but 5 is not greater than 8

Step 1: Evaluate the left-hand side of the conjunction (AND operator):
$$\text{18 is a multiple of 3}$$
This statement is true since 18 divided by 3 equals 6.

Step 2: Evaluate the right-hand side of the conjunction (AND operator):
$$\text{5 is not greater than 8}$$
This statement is true since 5 is indeed not greater than 8.

Step 3: Evaluate the truth value of the conjunction:
Since both statements in the conjunction are true, the whole statement is true.

Answer: The truth value of proposition r is true.

d) s: It is not the case that 10 is a multiple of 3 or that 5+4<10

Step 1: Evaluate the left-hand side of the disjunction (OR operator):
$$\text{10 is a multiple of 3}$$
This statement is false since 10 is not divisible by 3.

Step 2: Evaluate the right-hand side of the disjunction (OR operator):
$$\text{5+4<10}$$
This statement is true since 5+4 equals 9 which is less than 10.

Step 3: Evaluate the truth value of the disjunction:
Since one of the statements in the disjunction is true, the whole statement is true.

Answer: The truth value of proposition s is true.

e) t: Mariano Melgar was a writer as well as a musician

This proposition is based on a fact or historical information and cannot be determined purely by logical evaluation. It is not a mathematical statement, therefore we cannot assign a truth value to it.

Answer: The truth value of proposition t cannot be determined.