Venn Diagrams and Logic

Front

What is a Venn Diagram?

Back

A Venn Diagram is a visual representation of the relationships between different sets, using overlapping circles to show commonalities and differences.

Front

What does the symbol ∼ represent in logic?

Back

The symbol ∼ represents negation, indicating that the statement is not true.

Front

What does the symbol ∧ represent in logic?

Back

The symbol ∧ represents logical conjunction, meaning 'and'. It is true only if both statements are true.

Front

What does the symbol ∨ represent in logic?

Back

The symbol ∨ represents logical disjunction, meaning 'or'. It is true if at least one of the statements is true.

Front

What does the symbol → represent in logic?

Back

The symbol → represents logical implication, meaning 'if... then'. It indicates that if the first statement is true, then the second statement must also be true.

Front

What is the shaded region in a Venn Diagram representing p ∧ q?

Back

The shaded region represents the intersection of sets p and q, where both conditions are true.

Front

How do you find the number of students who chose only one subject in a Venn Diagram?

Back

To find the number of students who chose only one subject, subtract the number of students who chose multiple subjects from the total for that subject.

Front

What is the formula for the total number of elements in a union of two sets?

Back

The formula is |A ∪ B| = |A| + |B| - |A ∩ B|, where |A| and |B| are the number of elements in sets A and B, respectively.

Front

What does the shaded region in a Venn Diagram representing ∼p ∧ ∼q indicate?

Back

It indicates the area outside both sets p and q, meaning neither condition is true.

Front

How can you represent the number of students who took both French and Spanish in a Venn Diagram?

Back

This is represented by the intersection of the two circles for French and Spanish.