Question

For the statement "if Fury is the director of SHIELD then Hill and Coulson are SHIELD agents" (a) Write the contrapositive (b) Write the converse (c) Write the inverse (d) Write the negation

Answer 1

Explanation:

Consider the provided information.

If Fury is the director of SHIELD then Hill and Coulson are SHIELD agents." For the condition statement or equivalent "If p then q"

The rule for Converse is: Interchange the two statements.

The rule for Inverse is: Negative both statements.

The rule for Contrapositive is: Negative both statements and interchange them.

The rule for Negation is: If p then q" the negation will be: p and not q.

- Part (A) Write the contrapositive.

.Here p is Fury is the director of SHIELD, and q is Hill and Coulson are SHIELD agents.

Contrapositive: If Hill and Coulson are not SHIELD agents, then Fury is not the director of SHIELD.

- Part (b) Write the converse.

.Here p is Fury is the director of SHIELD, and q is Hill and Coulson are SHIELD agents.

.Converse: If Hill and Coulson are SHIELD agents, then Fury is the director of SHIELD.

- Part (c) Write the inverse.

.Here p is Fury is the director of SHIELD, and q is Hill and Coulson are SHIELD agents.

.Inverse: If Fury is not the director of SHIELD then Hill and Coulson are not SHIELD agents

- Part (D) Write the negation.

.Here p is Fury is the director of SHIELD, and q is Hill and Coulson are SHIELD agents.

.Negation: Fury is the director of SHIELD and Hill and Coulson are not SHIELD agents"

Answer 2

Explanation:

Consider the provided information.

If Fury is the director of SHIELD then Hill and Coulson are SHIELD agents"

For the condition statement
`p \rightarrow q` or equivalent "If p then q"

• The rule for Converse is: Interchange the two statements.
  `q \rightarrow p`
• The rule for Inverse is: Negative both statements.
  `\sim p \rightarrow \sim q`
• The rule for Contrapositive is: Negative both statements and interchange them.
  `\sim q \rightarrow \sim p`

• The rule for Negation is: If p then q" the negation will be: p and not q.
  `p \rightarrow q=\sim p\vee q=p\vee \sim q`

Part (A) Write the contrapositive.

Here p is Fury is the director of SHIELD, and q is Hill and Coulson are SHIELD agents.

Contrapositive: If Hill and Coulson are not SHIELD agents, then Fury is not the director of SHIELD.

Part (b) Write the converse.

Here p is Fury is the director of SHIELD, and q is Hill and Coulson are SHIELD agents.

Converse: If Hill and Coulson are SHIELD agents, then Fury is the director of SHIELD.

Part (c) Write the inverse.

Here p is Fury is the director of SHIELD, and q is Hill and Coulson are SHIELD agents.

Inverse: If Fury is not the director of SHIELD then Hill and Coulson are not SHIELD agents

Part (D) Write the negation.

Here p is Fury is the director of SHIELD, and q is Hill and Coulson are SHIELD agents.

Negation: Fury is the director of SHIELD and Hill and Coulson are not SHIELD agents"