Minimum wages are an ineffective tool to tackle poverty because they don’t keep pace with inflation. The minimum wage is set to a fixed amount. Unless legislators revisit the minimum wage each year and make adjustments for inflation and real wage growth, those earning the legal minimum wage will fall behind.
The evolution of the federal minimum wage in the United States illustrates the dangers of relying on a legal minimum wage to tackle poverty. In 1968, the federal minimum wage guaranteed a full-time worker an income of $19,553 a year; enough to keep a family of three (two parents and one child) above the national poverty line.  By 2013, inflation and wage growth in real terms meant that the federal minimum wage was no longer sufficient to sustain a family of three. The minimum wage guaranteed a full-time worker just $15,080 a year. This would not even be sufficient to keep a family of two (one adult and one child) above the poverty line.
A minimum wage can keep place with inflation if it is designed with automatic increases on par with the rate of inflation. This would ensure that every full-time worker received a pay increase that matched the rate of inflation each year, allowing them to retain their purchasing power.
[P1] A fixed minimum wage doesn't keep pace with inflation. [P2] Therefore, even with a minimum wage, many workers will still not earn enough to keep their families from poverty. [P3] Therefore, a minimum wage is ineffective at combating poverty.
Rejecting the premises
[Rejecting P1] A minimum wage can keep pace with inflation.