QuestionCesimplfy $\begin{array}{l} Q(P \Rightarrow P) \Rightarrow \neg(Q \Rightarrow(Q) \\ T \Rightarrow \neg(\neg 6 \Rightarrow Q) \\ T \Rightarrow \neg(\neg T) \\ T \Rightarrow \neg F \end{array}$ $T \Rightarrow I$ always true (2) $(7 P \wedge \varphi) \vee(\neg P \wedge Q)$
Q/Find the converse and contrapositive "If Muna is studing for the mid-term exam then it is not hoilday time

Studdy Solution

STEP 1

1. We are given a logical statement and need to find its converse and contrapositive.
2. The statement is: "If Muna is studying for the mid-term exam then it is not holiday time."
3. We assume standard definitions of converse and contrapositive in logic.

STEP 2

1. Identify the components of the given statement.
2. Construct the converse of the statement.
3. Construct the contrapositive of the statement.

STEP 3

Identify the components of the given statement:
- Let $P$ be "Muna is studying for the mid-term exam." - Let $Q$ be "It is not holiday time."
The statement can be expressed in logical terms as:
$P \Rightarrow Q$

STEP 4

Construct the converse of the statement:
The converse of an implication $P \Rightarrow Q$ is $Q \Rightarrow P$ .
In words, the converse is:
"If it is not holiday time, then Muna is studying for the mid-term exam."

STEP 5

Construct the contrapositive of the statement:
The contrapositive of an implication $P \Rightarrow Q$ is $\neg Q \Rightarrow \neg P$ .
In words, the contrapositive is:
"If it is holiday time, then Muna is not studying for the mid-term exam."
The converse is: "If it is not holiday time, then Muna is studying for the mid-term exam."
The contrapositive is: "If it is holiday time, then Muna is not studying for the mid-term exam."

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