Prove That $( q \wedge ( p \rightarrow \neg q ) ) \rightarrow \neg p$

question 109

Short Answer

Prove that $( q \wedge ( p \rightarrow \neg q ) ) \rightarrow \neg p$ is a tautology using propositional equivalence and the laws of logic.

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Definitions:

Earned Income Credit

A refundable tax credit for low to moderate-income working individuals and families, particularly those with children.

Qualifying Child

A dependent of a taxpayer who meets specific IRS criteria for age, relationship, residency, and support for tax benefits.

Retirement Savings

Funds accumulated for retirement, often involving tax advantages, through vehicles such as 401(k) plans, IRAs, or annuities.

AGI

Adjusted Gross Income, an individual's total gross income minus specific deductions, used in the United States tax system to determine taxable income.