LEARJET DEPARTS ARPT UNDERLYING CLASS B AIRSPACE QUICKLY FOLLOWED BY UNAUTH ENTRY INTO CLASS B.

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TWR INSTRUCTED US TO MAINTAIN RWY HEADING UNTIL 1900 FT. UPON REACHING 1900 FT THEY ADVISED US TO SWITCH TO 125.35 CLEVELAND APCH FOR INFLT ADVISORIES (WE WERE VFR). WE STARTED A GRADUAL TURN TO THE L WHILE I WAS SWITCHING THE RADIO FREQ. AS I CALLED APCH I SWITCHED OVER THE TRIMBLE 2101 GPS IN THE ACFT TO THE AIRSPACE MODE TO ALERT US IF WE GOT TOO CLOSE TO CLEVELAND'S CLASS B AIRSPACE. THE ACFT WAS CLBING QUICKLY. UPON GETTING A RESPONSE FROM CLEVELAND THEY ADVISED US WE WERE IN CLASS B AIRSPACE. AT THAT TIME WE WERE ADVISED OF SEVERAL TARGETS IN OUR AREA. I DID NOT LOOK AT THE GPS ANY LONGER; I CONCENTRATED ON LOOKING FOR TFC; WE WERE ASKED TO FLY A 090 DEG HDG. A LOT OF THINGS HAPPENED IN A VERY SHORT TIME. WE WERE ONLY A COUPLE OF MI AWAY FROM THE ARPT. I KNEW THE CLASS B CAME UP SHORTLY AFTER TKOF; THAT IS THE REASON FOR THE GPS AIRSPACE ALERT PAGE I WAS BRINGING UP. AS IT STOOD I NEVER DID GET A CONFIRMATION FROM OUR GPS. WE ENTERED THE CLASS B. I BELIEVE CLEVELAND APCH NEVER WOULD HAVE SAID WE WERE IN THEIR AIRSPACE IF WE WEREN'T AT LEAST CLOSE TO THEIR CLASS B TFC. AFTER THIS FLT WAS OVER I RECEIVED THE CHART CONCERNING THE CLASS B AIRSPACE (SECOND RING) AREA W OF CUYAHOGA COUNTY ARPT. I CAN HONESTLY SAY IT WAS CLOSE BUT I BELIEVE WE WERE OUTSIDE OF THE AIRSPACE. THIS ARPT IS VERY CLOSE TO THE CLASS B AIRSPACE. I WOULD SUGGEST WBOUND DEP FROM CGF HAVE CLASS B CLRNC BEFORE TKOF FOR VFR FLTS. OUR GPS HAS THE LATEST NAVDATA CARD AND HAS BEEN VERY RELIABLE. WE ARE GOING TO OBSERVE IT CLOSELY TO NOTE ANY IRREGULAR INDICATIONS. I HAVE SEEN NO REASON TO BELIEVE IT WAS IN ERROR. IT IS IFR CERTIFIED.