Please type your answer **Logical Analysis of Statements****Objective:** Analyze the logical form of the statements provided.**Let:**- \( W \): "It is Wednesday"- \( S \): "I will go shopping"- \( M \): "I will go to a movie"**Statements:**a. **If it is Wednesday, then I will go shopping and I will not go to a movie.** - **Logical Form:** \( W \rightarrow (S \land \neg M) \)**Analysis of Additional Statements:**b. **I will go shopping only if it is Wednesday and I will not go to a movie.** - **Logical Form:** \( S \rightarrow (W \land \neg M) \)c. **I will go shopping and not go to a movie is a sufficient condition for it to be Wednesday.** - **Logical Form:** \( (S \land \neg M) \rightarrow W \)d. **I will go shopping and not go to a movie is a necessary condition for it to be Wednesday.** - **Logical Form:** \( W \rightarrow (S \land \neg M) \)**Task:** For each of the statements (b, c, and d), determine whether it is logically equivalent to statement (a) or its converse.

Name: Please type your answer **Logical Analysis of Statements****Objective:
Uploaded: 2024-03-20T07:07:37.000Z
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Description: Please type your answer **Logical Analysis of Statements****Objective:** Analyze the logical form of the statements provided.**Let:**- \( W \): "It is Wednesday"- \( S \): "I will go shopping"- \( M \): "I will go to a movie"**Statements:**a. **If it

Here, W represents "it is Wednesday" , S represents " I will go shopping" and M represents "I will go to a movie". a) The statement says if W then S∧~M The truth table for the above statement is given as W S M ~M S∧~M W→S∧~M T T T F F F T T F T T T T F T F F F T F F T F F F T T F F T F T F T T T F F T F F T F F F T F TConverse of statement a) i.e., if S∧~M then W The truth table is as follows: W S M ~M S∧~M S∧~M→W T T T F F T T T F T T T T F T F F T T F F T F T F T T F F T F T F T T F F F T F F T F F F T F T b) The second statement says S only if W∧~M i.e., if S then W∧~M The truth table is given as : W S M ~M W∧~M S→W∧~M T T T F F F T T F T T T T F T F F T T F F T T T F T T F F F F T F T F F F F T F F T F F F T F T Thus, statement b) is not equivalent to either a or its converse.c) The third statement says S∧~M is a sufficient condition for it to be Wednesday. i.e., if S∧~M then W. The truth table is as follows: W S M ~M S∧~M S∧~M→W T T T F F T T T F T T T T F T F F T T F F T F T F T T F F T F T F T T F F F T F F T F F F T F T Thus, statement c is equivalent to the converse of statement a.d) The fourth statement says S∧~M is a necessary condition for it to be Wednesday. i.e., if W then S∧~M The truth table is as follows: W S M ~M S∧~M W→S∧~M T T T F F F T T F T T T T F T F F F T F F T F F F T T F F T F T F T T T F F T F F T F F F T F T Thus, statement d is equivalent to statement a.