Question

homework 2 - 1 conditional statements
let p represent \daniel is angry\, and let q represent \daniel is not having fun\.
translate the following into symbolic form.

1. daniel is not angry
2. daniel is angry and daniel is not having fun
3. daniel is not angry or daniel is not having fun.

translate the following from symbolic form to written form.

1. p ∧ ¬q
2. ¬q ∨ p

write the converse of each of the following conditional statements.

1. if two angles are adjacent, then they share a common ray.

converse:

1. if m is the mid - point of ab, then m is between a and b and am = mb.

converse:

Explanation:

Step1: Recall logical - negation symbol

The symbol for "not" in logic is $
eg$. Given $p$ represents "Daniel is angry", "Daniel is not angry" is $
eg p$.

Step2: Recall logical - and symbol

The symbol for "and" in logic is $\wedge$. Given $p$ represents "Daniel is angry" and $q$ represents "Daniel is not having fun", "Daniel is angry and Daniel is not having fun" is $p\wedge q$.

Step3: Recall logical - or symbol

The symbol for "or" in logic is $\vee$. Given $p$ represents "Daniel is angry" and $q$ represents "Daniel is not having fun", "Daniel is not angry or Daniel is not having fun" is $
eg p\vee q$.

Step4: Translate symbolic to written form

Given $p$ represents "Daniel is angry" and $q$ represents "Daniel is not having fun", $p\wedge
eg q$ means "Daniel is angry and Daniel is having fun".

Step5: Translate symbolic to written form

Given $p$ represents "Daniel is angry" and $q$ represents "Daniel is not having fun", $
eg q\vee p$ means "Daniel is having fun or Daniel is angry".

Step6: Recall converse of conditional statement

The converse of a conditional statement "If $a$, then $b$" is "If $b$, then $a$". For "If two angles are adjacent, then they share a common ray", the converse is "If two angles share a common ray, then they are adjacent".

Step7: Recall converse of conditional statement

For "If $M$ is the mid - point of $AB$, then $M$ is between $A$ and $B$ and $AM = MB$", the converse is "If $M$ is between $A$ and $B$ and $AM = MB$, then $M$ is the mid - point of $AB$".

Answer:

1. $

eg p$

1. $p\wedge q$
2. $

eg p\vee q$

1. Daniel is angry and Daniel is having fun.
2. Daniel is having fun or Daniel is angry.
3. If two angles share a common ray, then they are adjacent.
4. If $M$ is between $A$ and $B$ and $AM = MB$, then $M$ is the mid - point of $AB$.