Algebra - Truth Table

Choose the correct conclusion and why.

Choose the one alternate that best completes the statement or answers the question.
1. As a special promotion, the Green Thumb organic foods chain said that everyone who came to one of their stores between noon and 1pm on January 4 would be offered a free loaf of 23-grain bread. They did not keep this promise . Therefore, between noon and 1pm on January 4:

a. No one who came to a Green Thumb store was offered a free loaf of 23 -grain bread.
b. At least one person who came to a Green Thumb store was not offered a free loaf of 23 -grain bread.
c. At least one person who came to a Green Thumb store was offered a free loaf of 23 -grain bread.
d. The Green Thumb chain ran out of 23 -grain bread.

2. In a statement to the press, a representative of a tobacco company stated " In our years of research, we never discovered a link between cancer and smoking" That statement was later found to be false. Therefore, in their years of research:

a. The tobacco company sometimes did not discover a link between cancer and smoking.
b. The tobacco company sometimes discovered a link between cancer and smoking.
c. The tobacco company never discovered a link between cancer and smoking
d. The tobacco company always discovered a link between cancer and smoking.

Translate the argument into symbolic form . Then use a truth table to determine whether the argument is valid or invalid. ( Ignore differences in past , present , and future tense)

3. If Emilio and Rodrigo both cook, then the meal is tasty.

Emilio cooked and the meal was not tasty.
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. . Rodrigo did not cook