Question

Let p and q be statements. Which of the following implies that p ∨ q is false?
a. ¬ p ∨ ¬q is false.
b. ¬ p ∨ q is true.
c. ¬ p ∧ ¬q is true.
d. p ⇒ q is true.
e. p ∧ q is false.

Answer 1

Answer:

option d

Step-by-step explanation:

e. p ∧ q is false is correct

Answer 2

Answer:

The given statement pvq is false and  

option (c) p'∧q' is true for same values of p and q, where both p and q are false.

Step-by-step explanation:

Basic Logical Operators:

In mathematics, three logical operators are employed:

• Conjunction (AND)
• Disjunction (OR)
• Negation (NOT)

Conjunction:

• The "AND" operator allows us to combine two statements. It also goes by the name of a conjunction.
• The symbol for it is "∧" If any of the statements in this operator are false, the result will also be false.
• The conclusion will be accurate if both assertions are true. It has one output but two or more inputs.

Disjunction:

• The "OR" operator can be used to connect two statements. It also goes by the name disjunction.
• The symbol for it is "∨" If any of the statements in this operator are true, the outcome is true. If both the statements are false, then the result will be false. It has one output but two or more inputs.

Negation:

• The "OR" operator can be used to connect two statements. It also goes by the name disjunction.
• The symbol for it is "'" If any of the statements in this operator are true, the outcome is true. The conclusion will be false if any or both of the statements are false. It has one output but two or more inputs.

Let p and q are two statements then

     pvq is false if both p and q are false.

  a) p'∨q' is false if both p and q is true.

  b) p'∨q is true if p is true and q is false.

  c) p'∧q' is true if both p and q are false.

  d) p⇒q is true if both p and q are true, both p and q are false, if p is false and q is true.

  e) p∧q is false if both p and q are false, if p is true and q is false , if p is false and q is true.

Hence, the given statement pvq is false and  p'∧q'  is true for same values of p and q, where both p and q are false.

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